5.1
Using imperial Units for capacity
try these
You will need
• measuring
containers with
imperial units
(optional)
capacity
the amount that
a container can
hold
Hint
If possible, look at
actual measuring
containers to
compare the sizes
of the units.
ReflectiNg
How are the
British and
American imperial
units different for
capacity? How are
they the same?
i) 1  12 =
3
1
2
ii) 1 ÷ 2 =
4
or 0.5
At a marina, Jo measures oil and gas for outboard motors using
imperial units. How are these units for capacity related?
Imperial Units for Capacity (American and British)
Unit
Relationships (US)
Relationships (UK)
fluid ounce (fl oz)
1 fl oz  2 T (tablespoons)
1 fl oz  2 T (tablespoons)
1 c  8 fl oz
1 c  10 fl oz
cup (c)
pint (pt)
1 pt  2 c, or
16
fl oz
1 pt  2 c, or
20
fl oz
quart (qt)
1 qt  2 pt, or
32
fl oz
1 qt  2 pt, or
40
fl oz
gallon (gal)
1 gal  4 qt, or
128
fl oz
1 gal = 4 qt, or
160
fl oz
1
How many pints are in a gallon?
1 qt =
pt and 1 gal =
qt, so
2
4
pt/qt ×
qt/gal =
pt in 1 gal
2
8
4
2
1 gal =
8
pt, so 1 pt =
1
gal
8
Example 1
Evan is making punch for hospital volunteers. He needs
1
3 2 quarts of cranapple juice. How many cups is this?
Solution
A. How many cups are in a quart?
2c=
pt and
pt =
1
2
c/pt ×
pt/qt =
2
2
4
1
qt, so
c in 1 qt
1
B. How many cups are in 3 2 quarts?
1
qt × 4 c/qt = 12 c and 2 qt × 4 c/qt = 2
c+
c = 14 c of cranapple juice
12
2
3
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Example 2
Hints
• Bushel (bu) is
a unit for dry
measures.
1 bu = 8 gal
• The relationships
for liquid
measures can
be used for dry
measures.
Lars bought a bushel of oats for his horses. If he uses 1 pt
of oats each day, how many days will the oats last?
Solution
1 gal = 4
qt and 1 qt =
2
pt, so 1 gal =
1 bu =
gal, so 1 bu =
8
gal ×
8
8
pt
8
pt/gal, or
64
pt
1 bu of oats will last 64 days.
Practice
Hint
1. Express each capacity in the units given.
a) 1 c =
b) 3 fl oz =
c) 4 gal =
1
2
pt
6
512
T
fl oz (US)
d) 4 gal =
640
fl oz (UK)
e) 7 bu =
56
gal
1
f) 3 2 bu =
112
qt
Think about
whether the
answer should be
greater than or less
than the number
given.
2. Express each capacity in cups.
a) a can of beans, 19 fl oz (US)
between
2
c and
3
c
b) a can of fruit, 14 fl oz (UK)
between
1
c and
2
c
2 cups
13/4 cup
11/2 cup
11/4 cup
1 cup
3/
4
3. Complete the statement using >, <, or =.
1/
2
1/
4
1 c (UK) > 1 c (US), so 1 bu (US) > 1 bu (UK)
4. Olga is making perogies for Canada’s National Ukrainian
Festival in Dauphin, Manitoba. She is tripling this recipe.
a) How many cups of flour does Olga need?
3 x 5 c = 15 c
Olga needs 15 c of flour.
16 oz
14 oz
12 oz
10 oz
8 oz
6 oz
4 oz
2 oz
Dough for Perogies
(in US measures)
5 c flour
2 T salt
1/3 c vegetable oil
2 c warm water
b) How many fluid ounces (US) of oil does she need?
3 x 31 c = 1 c
Olga needs 8 fl oz (US) of vegetable oil.
5. Connor has a bottle with 2 fl oz (US) of gold paint for
repairing picture frames. How many tablespoons of paint is
this?
AW10
1 fl oz = 2 T, so 2 fl oz x 2 T/fl oz =0-17-650271-8
4 T
Figure Number
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The bottle contains 4 T of gold paint.Company
Technical
Pass
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Chapter 5
1st Pass
Capacity,
ApprovedVolume, Mass, and Temperature
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5.2
Using Metric Units for capacity
try these
You will need
• measuring
containers with
metric units
(optional)
i) 1.2 × 102 =
120
iii) 0.8 × 104 =
ii) 3.5 × 103 =
3500
iv) 96 × 1023 = 0.096
8000
Mitchell is pouring orange juice from a 2 L carton into 300 mL
bottles to put in his cooler. How many bottles can he fill?
Metric (SI) Units for Capacity
Relationship to litre
Unit
ReflectiNg
kilolitre (kL)
Compare this
chart to the one
you used for
metric units for
length (in
Chapter 2). How
are they the
same? How are
they different?
Which units in the
chart are most
commonly used?
1 kL = 1000 L or 103 L
hectolitre (hL)
1 hL = 100 L or
102
L
decalitre (daL)
1 daL = 10 L or
101
L
litre (L)
decilitre (dL)
1 dL = 0.1 L or
centilitre (cL)
1 cL = 0.01 L or
millilitre (mL)
1 mL = 0.001 L or
1
10
1
100
1
1000
1
How many millilitres are in 2 L?
1 L = 1000 mL, so 2 L = 2000 mL
2
How many bottles can Mitchell fill?
2000 mL ÷ 300 mL/bottle = 6.666...
Mitchell can fill
6
L
L
L
bottles.
Example
680 mL
Cong ordered a case of 12 cans of pasta sauce. How many litres
of sauce did he order?
Solution
A. What is the total capacity in millilitres?
12 cans × 680 mL/can = 8160 mL
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B. What is the capacity in litres?
1000 mL = 1 L, so 1 mL = 0.001 L
8160 mL × 0.001 L/mL = 8.16 L
Cong ordered 8.16 L of sauce.
Hint
Think about
whether the
answer should
be greater or less
than the number
given.
Practice
1. Express one litre in different ways.
a) 1 L =
10
dL, or
b) 1 L =
0.1
daL, or
cL, or
100
0.01
mL
1000
hL, or 0.001 kL
2. Express each capacity in litres.
a) a jar of salsa, 650 mL
0.65
L
b) a bottle of eyeglass lens cleaner, 60 mL
0.06
L
c) a can of brass polish, 142 mL
0.142 L
3. Compare. Write >, <, or = to make a true statement.
a) 5.64 L > 564 mL
c) 9.2 daL = 92 L
b) 3.1 dL < 31 L
d) 4 cL < 400 mL
4. Write each capacity using litres and millilitres.
a) a bottle of floor cleaner, 2800 mL
2
L
800
mL
b) a pet’s bowl of water, 3.6 L
3
L
600
mL
c) gas for a lawn mower, 5.04 L
5
L
40
mL
5. How many litres of juice are in the six-pack?
6 x 946 mL = 5676 mL
1 mL = 0.001 L, so 5676 mL x 0.001 L/mL = 5.676 L
946 mL
946 mL
946 mL
6. It costs about $2 to flush a toilet 50 times, using 0.5 L
of water each time. Determine each cost.
a) for 150 flushes in a week
e.g., 3 x ($2 for 50 flushes) = $6
b) for flushes using a total of 100 L
e.g., 50 flushes use 50 x 0.5 L = 25 L.
100 L  (25 L for $2) = 4 groups of $2, or $8
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5.3
capacity in Different Systems
try these
You will need
Circle the metric units. Underline the imperial units.
• measuring
containers with
imperial and
metric units
(optional)
pint
cup
litre
quart
fluid ounce
millilitre
Adèle is heating 5 qt (US) of soup for an out-of-the-cold dinner. A
can of soup contains 540 mL. How many cans does Adèle need?
Hint
If possible, look
at measuring
containers to
compare their
sizes.
SI to Imperial (US)
∙ 0.03 fl oz
1 mL =
∙ 29.57 mL
1 fl oz =
∙ 2.11 pt
1L=
∙ 0.47 L, or
1 pt =
470
mL
∙ 1.06 qt
1L=
∙ 0.95 L, or
1 qt =
950
mL
∙ 0.26 gal
1L=
1
Imperial (US) to SI
1 gal
=∙
3.79 L, or
3790 mL
How many millilitres of soup are there? 1 qt =∙
950 mL
? mL ∙ 950 mL
=
1 qt
5 qt
5
×
? mL ∙ 950 mL
=
×
1 qt
5 qt
? =∙
ReflectiNg
Why do you need
to round up the
number of cans?
Which imperial
system, US or UK,
is more commonly
used for capacity
in Canada?
2
4750
1
5
, or 4750 mL
How many cans of soup does Adèle need?
4750 mL ÷ 540 mL/can = 8.796...cans
Adèle needs
9 cans of soup.
Example
Eli is installing a hot water tank with a capacity of 153 L. What is
the capacity of the tank, to the nearest gallon?
Solution
1 L =∙
0.26 gal
153 L ×
0.26 gal/L =∙
39.78 gal
40 gal.
The capacity of the tank is about
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Practice
1. Express each capacity in the units given.
a) a can of corn, 12 fl oz =∙ 355 mL
b) a soup kettle, 10 L =∙ 2.6 gal, to the nearest tenth
c) a tube of toothpaste, 130 mL =∙
fl oz
4
d) a can of varnish, 1 L =∙ 2.11 pt or 1.06 qt
Note
Use US units in all
questions.
2. What can you multiply by to change one unit to the other?
a) litres to pints x 2.11 c) gallons to litres x 3.79
b) pints to litres x 0.47 d) litres to gallons x 0.26
3. Astrid’s jeep uses 8.9 L of gas for 100 km of city driving and
7.2 L for 100 km of highway driving. About how many gallons
would the jeep use in each case? (Round to one decimal
place.)
a) for 100 km of highway driving
e.g., 7.2 L x 0.26 gal(US)/L =· 1.872 gal (US)
The jeep would use about 1.9 gal of gas.
b) for 100 km of city driving
e.g., 8.9 L x 0.26 gal/L =· 2.314 gal
The jeep would use about 2.3 gal of gas.
4. Latoya measured a room. She used an online calculator
to determine that she needs 4.28 gal of paint.
a) How many litres of paint does Latoya need?
PAINT
e.g., 1 gal =· 3.79 L, so
4.28 gal x 3.79 L/gal =· 16.2212 L
b) How many cans of paint should she buy?
3.67 L
e.g., 16.221 L  3.67 L/can = 4.419…
Latoya should buy 5 cans of paint.
5. Complete this label for a jar of pickles.
What relationship will you use?
e.g., 1 mL =· 0.03 fl oz
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5.4
Using imperial Units for Volume
try these
You will need
i) 1 yd =
• a yardstick or
tape measure
(imperial units)
volume
the amount of
space occupied
by a 3-D object
ii) 1 ft =
iii) 1 yd =
ft
3
iv) 1 ft =
in.
12
in.
36
1
3
yd
Ty is a part-time florist and gardener. He uses about 1000 cu in. of
pebbles in each planter he creates. The volume of pebbles in his
supply bin is 4 cu ft. How many planters can he fill?
Imperial Units for Volume
Unit
Relationships
cubic inches
(cu in.)
1 cu in. = 1 in. × 1 in. × 1 in.
1 cu ft = 1 ft × 1 ft × 1 ft
1 cu ft = 12 in. × 12 in. × 12 in., or 1728 cu in.
cubic feet
(cu ft)
cubic yards
(cu yd)
1 cu yd =
3
1 cu yd = 1 yd × 1 yd × 1 yd
ft × 3 ft × 3 ft, or
27
1
How many cubic inches of pebbles does Ty have?
4 cu ft × 1728 cu in./cu ft =∙ 6912 cu in.
2
How many planters can Ty fill?
6912 cu in. ÷ 1000 cu in./planter = 6.912
Ty can fill
planters.
6
cu ft
Example
Kyle, a bricklayer, needs 245 cu ft of lime to use in mortar. How
many whole cubic yards of lime does Kyle need to buy?
ReflectiNg
How can you use
an equation to
determine the
number of cubic
yards?
132
05C05.indd 132
Solution
1 cu yd =
245 cu ft ÷
27
27
Kyle needs to buy
cu ft
cu ft/cu yd = 9.074... cu yd of lime
10
Apprenticeship and Workplace 10
cu yd of lime.
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:25 PM
Practice
1. Express each volume in the units given.
a) 3 cu yd =
81
b) 54 cu ft =
2
c) 2 cu ft = 3456 cu in.
1
d)
cu yd =
cu ft
9
3
cu ft
cu yd
1
2. Eva wants to rent a cargo trailer with a volume of 7 2 cu yd
to move the contents of her store to a new location. She
researched some possible sizes. Express each volume below,
1
to one decimal place. Circle the volume closest to 7 2 cu yd.
a) 396 cu ft =∙
14.7
cu yd
c) 208 cu ft =∙
7.7
cu yd
b) 230 cu ft =∙
8.5
cu yd
d) 142 cu ft =∙
5.3
cu yd
Hint
Think about
whether the
answer should be
greater or less than
the number given.
3. The volume of Samantha’s hockey bag is 8288 cu in. What is
the volume to the nearest tenth of a cubic foot?
e.g., 1 cu ft = 1728 cu in.
8288 cu in.  1728 cu in./cu ft = 4.796… cu ft, or about 4.8 cu ft
The volume of Samantha’s hockey bag is about 4.8 cu ft.
4. Ryan is using his wheelbarrow to move topsoil to a garden.
His wheelbarrow holds 3 cu ft of soil. How many cubic yards
can Ryan take in 32 loads? (Round to the nearest tenth.)
e.g., volume taken: 32 loads x 3 cu ft/load = 96 cu ft
1 cu yd = 27 cu ft, so
96 cu ft  27 cu ft/cu yd = 3.555… cu yd
Ryan can take about 3.6 cu yd.
5. Aneta is delivering 12 cu yd of gravel to a
construction site. Her truck can hold 48 cu ft of
gravel. How many trips will she need to make?
e.g., 1 cu yd = 27 cu ft, so
12 cu yd x 27 cu ft/cu yd = 324 cu ft
324 cu ft  48 cu ft/trip = 6.75 trips
Aneta will need to make 7 trips.
6. List objects in your classroom that have a volume
between 1 cu ft and 1 cu yd.
Hint
Use a ruler or
measuring tape.
e.g., a desk, a filing cabinet
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5.5
Using Metric Units for Volume
try these
You will need
1 000 000 000
i) 1000 × 1000 × 1000 = ___________________,
or 10 9 , or 1 billion
• a metre stick or
tape measure
with metric units
0.000 001
ii) 0.01 × 0.01 × 0.01 = ___________________,
or 10 -6 , or 1 millionth
Henrik is making modelling clay for the 100 children in a daycare
centre. He allows 500 cm3 of modelling clay per child. Will all the
modelling clay fit into a storage container that holds 0.1 m3?
Metric (SI) Units for Volume
Unit
cubic kilometre (km3)
ReflectiNg
What patterns do
you see in the
chart?
Compare this
chart to the one
you used for
capacity. How are
they the same?
How are they
different?
Which units in the
chart are most
commonly used?
cubic hectometre (hm3)
cubic decametre (dam3)
cubic decimetre (dm3)
1 dm3 = 0.1 m × 0.1 m × 0.1 m, or
0.001 m3
cubic centimetre (cm3)
1 cm3 = 0.01 m × 0.01 m × 0.01 m, or
cubic metre (m3)
cubic millimetre (mm3)
0.000 001 m3
1 mm3 = 0.001 m × 0.001 m × 0.001 m
= 0.000 000 001 m3
How many cubic metres are needed for all the clay?
500 cm3 × 100 = 50 000 cm3
1 cm3 =
m3
0.000 001
0.000 001
cm3 ×
m3/cm3 = 0.05
50 000
m3
Will the modelling clay fit in the container?
0.05 m3 < 0.1 m3, so yes, the modelling clay will fit.
Example
•
•
05C05.indd 134
1 hm3 = 100 m × 100 m × 100 m, or 1 000 000 m3
1 000 m3
2
134
1 km3 = 1 000 m × 1 000 m × 1 000 m
= 1 000 000 000 m3
1 dam3 = 10 m × 10 m × 10 m, or
1
Hint
Volume of a
rectangular prism
= length × width ×
height
Relationship to cubic metre
What is the volume of an aquarium with 17 cm width,
35 cm length, and 23 cm height?
How much water does it hold? (1 cm3 = 1 mL)
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:26 PM
B. What is the capacity of the aquarium in litres?
1
mL, so 13 685 cm3 = 13 685 mL
1 cm3 =
23 cm
Solution
A. What is the volume of the aquarium?
cm ×
cm ×
cm = 13 685 cm3
17
35
23
1 mL = 0.001 L, so 13 685 mL × 0.001 L/mL = 13.685 L
The aquarium holds
13.7
35 cm
17 cm
L of water, to one decimal place.
Practice
1. Compare. Write >, <, or = to make a true statement.
a) 480 cm3 > 480 mm3
c) 1 m3 = 1000 dm3
b) 1.2 dm3 < 1.2 dam3
d) 1 m3 = 109 mm3
Hint
Use the charts
inside the back
cover.
AW10
2. Dave is a welder. He is making0-17-650271-8
a 50 L gas tank, shaped like a
C05-F11-AW10.eps
Figure
Number
rectangular prism, for a custom car.
Company
Hint
1 mL = 1 cm
3
a) What is the volume of the tank
in cubic centimetres?
Technical
Pass
1st Pass
1 L = 1000 mL, so 50 L x 1000
mL/L = 50 000 mL, or 50 000 cm3
Approved
b) What might the dimensionsNot
ofApproved
the tank be, in centimetres?
e.g., 100 cm by 20 cm by 25 cm
3. The volume of a coffee mug is 226 cm3. How many mugs can
you fill from a pot that contains 2500 mL of coffee?
e.g., 1 cm3 = 1 mL, so 226 cm3 = 226 mL
2500 mL  226 mL/mug = 11.061… mugs
The pot fills 11 mugs.
4. A researcher claims that the average amount of fresh water
used in Canada is 125 m3 per person per year.
a) How much is this in cubic centimetres per person per day?
e.g., 125 x (100 cm x 100 cm x 100 cm) = 125 000 000 cm3/year
Hint
1 year = 365 days,
except in a leap
year
125 000 000 cm3  365 days = 342 465.7534 cm3/day
The average amount used is about 342 466 cm3/person/day.
b) How much is this in litres per person per day?
e.g., 342 466 cm3 = 342 466 mL
AW10
342 466 mL  1000 mL/L = 342.466
L
0-17-650271-8
Figure Number
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The average amount used is about Company
342 L/person/day.
Copyright © 2011 by Nelson Education Ltd.
Chapter 5
Technical
Capacity,
Volume, Mass,
Pass
1st and
PassTemperature
135
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Not Approved
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5.6
Volume in Different Systems
try these
You will need
Circle the metric units. Underline the imperial units.
• a metre stick or
tape measure
(imperial and
metric)
Hint
Use the charts
inside the back
cover to make
other conversions.
e.g., 1 m3 = ? cu ft
ReflectiNg
How could you
express the
capacity of the
backpack in
litres?
∙ 28.32 L)
(1 cu ft =
cubic yard
cubic centimetre
cubic inch
cubic mile
For a camping trip, Willow bought a backpack that has a volume
of 4577 cu in. What is its volume in cubic centimetres?
SI to Imperial
∙ 0.06 cu in.
1 cm3 =
=∙
3 ∙
1 km =
1 m3
1.31 cu yd
0.24 cu mi
Imperial to SI
∙ 16.39 cm3
1 cu in. =
=∙
∙
1 cu yd =
∙
1 cu mi =
1 cu ft
28.32 dm3
0.76 m3
4.17 km3
cu in. =∙
1
What relationship will you use?
2
What is the volume of the backpack?
4577 cu in. × 16.39 cm3/cu in. =∙
75 017.03
The backpack has a volume of about 75 017 cm3.
1
16.39 cm3
cm3
Example
Matt is the manager of an arena. He wants to buy 14 m3 of sand
to create beach volleyball courts in the arena after the skating
season ends. How many cubic yards of sand does he need?
Solution
How many cubic yards are there?
14
? cu yd =∙
14 m3
× ? cu yd =∙
14 m3
? =∙
The volume is
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18.3
Apprenticeship and Workplace 10
1
m3 =∙
1.31
cu yd
1.31 cu yd
1 m3
1.31 cu yd
1m
18.34
1
3
×
14
, or 18.34
cu yd
cu yd, to one decimal place.
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:27 PM
Practice
1. Complete the pattern.
Number of cubic metres
Number of cubic yards
1
2
3
1.31
2.62
3.93
4
5
5.24 6.55
2. What is the volume, to the nearest tenth of a unit?
a) a pile of firewood, 2 cu yd
1.5
m3
b) a room, 58 m3
76.0
cu yd
c) a pond, 0.8 cu mi
3.3
km3
d) Lake Athabasca, 110 km3
26.4
cu mi
3. Abdul, who works in construction, is shopping for a tool box.
What is each volume to the nearest cubic centimetre?
a) 1120 cu in.
18 357 cm3
b) 195 cu in.
3196
c) 1565 cu in.
cm3
25 650 cm3
4. A cabinet for wood-carving tools has a volume of 0.38 m3.
Compare this to the volumes of the tool boxes in Question 3.
Hint
1 m3
= 1 000 000 cm3
e.g., 1 m3 = 1 000 000 cm3, so
0.38 m3 = 380 000 cm3
The wood-carving cabinet is much bigger.
5. What can you multiply by to change one unit to the other?
a) cubic miles to cubic kilometres
x 4.17
b) cubic metres to cubic feet
x 35.37
c) cubic feet to cubic metres
x 0.03
Hint
1 cu yd = 27 cu ft
6. Justin estimates that he needs 100 m3 of space
to store the equipment for his snow-blowing
business. How many cubic feet of storage
space does he need?
e.g., 1 m3 =· 35.37 cu ft, so
100 m3 x 35.37 cu ft/m3 =· 3537 cu ft
Justin needs about 3537 cu ft of storage.
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Mid-chapter
Hint
Use the charts
inside the back
cover.
1. Compare. Write = or ≠ to make a true statement.
a) 8 bu ≠ 1 gal
c) 5 kL = 5000 L
b) 7 qt = 28 c
d) 4 cL ≠ 0.4 L
2. What is the capacity of each can in millilitres?
e.g., 1 L = 1000 mL
Large can: 3.43 L x 1000 mL/L = 3430 mL
PAINT
Small can: 0.86 L x 1000 mL/L = 860 mL
3.43 L
PAINT
0.86 L
3. Hans read on the Internet about a pickup truck with a fuel
tank capacity of 34 gal (US). Hans buys gas in litres. What is
the capacity in litres?
e.g., 1 gal =· 3.79 L, so 34 gal x 3.79 L/gal =· 128.86 L
The capacity is about 129 L.
4. Circle the greater volume in each pair.
a) 26 cu ft or 1 cu yd
1
b) 6912 cu in. or 2 2 cu ft
5. What can you multiply by to change one unit to the other?
a) cubic metres to cubic centimetres
x 1 000 000
b) cubic millimetres to cubic centimetres
x 0.001
5-F14-AW10.eps
6. Are there more cubic inches or cubic centimetres for the
same volume? Why? cubic centimetres, because they are smaller
t Pass
7. Madison sells cedar wood chips by whole cubic yards. A
customer wants 60 cu ft of the wood chips for a pathway.
How many cubic yards does the customer need?
e.g., 1 cu yd = 27 cu ft
60 cu ft  27 cu ft/cu yd = 2 cu yd and part of another cubic yard
The customer needs 3 cu yd of wood chips.
8. What is the volume of 8.4 cu yd of gravel, to the nearest tenth
of a cubic metre?
e.g., 1 cu yd =· 0.76 m3
8.4 cu yd x 0.76 m3/cu yd =· 6.384, or about 6.4 m3
138
05C05.indd 138
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Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:28 PM
Solving a capacity Puzzle
5.7
Franca has a small pail with a capacity of
3 quarts and a large pail with a capacity of
5 quarts.
A. How can Franca use the two pails to get
2 quarts of water?
e.g., Franca can fill the large pail (5 qt
in the large pail), then pour some of the
water from the large pail into the small pail
(3 qt in the small pail, 2 qt in the large
pail). Franca would have 2 qt in the large
pail.
B. How can Franca use the two pails to get
2 pints of water?
e.g., 2 pt = 1 qt, so Franca needs 1 qt of water.
Franca can fill the small pail (3 qt in the small pail), pour the
water from the small pail into the large pail (3 qt in the large
pail), fill the small pail again (3 qt in the small pail, 3 qt in the
large pail), and then pour as much water as possible from the
small pail into the large pail (3 qt – 2 qt = 1 qt in the small
pail; 3 qt +2 qt = 5 qt in the large pail). Franca would have
1 qt, which is 2 pt, in the small pail.
C. Suppose Franca had a blue pail with a capacity of 3 L and
a red pail with a capacity of 5 L, and she needs to measure
1000 mL of water. Would the solution be different? If so, how?
If not, why not?
No. The solution would be the same except the small pail (blue)
would have 3 L instead of 3 qt and the large pail (red) would
have 5 L instead of 5 qt. Franca would follow the same steps to
get 1 L, which is 1000 mL, in the small (blue) pail.
Copyright © 2011 by Nelson Education Ltd.
05C05.indd 139
Chapter 5
Capacity, Volume, Mass, and Temperature
139
4/17/10 12:30:28 PM
5.8
Using imperial Units for Mass
try these
You will need
i) 80  16 
• balance scales
and masses
or a scale with
imperial units
mass
the amount of
matter in an
object
ReflectiNg
Why does it make
sense that a UK
ton is called a
long ton and a
US ton is called a
short ton?
ii) 120  16 
iii) 4000  2000 
5
7.5
2
3
iv) 6720  2240 
Before paving a driveway, Josh needs to spread 3 cu yd of gravel.
The mass is about 8250 lb. How many tons is this?
Imperial Units for Mass
Unit
Relationships (US)
1
16
Relationships (UK)
1
16
ounces (oz)
1 oz 
pound (lb)
1 lb  16 oz
1 lb  16 oz
ton (T)
1 T  2000 lb
1 T  2240 lb
1
lb
1 oz 
What is the mass in US
tons, to one decimal place?
1 T (US) = 2000 lb, so
8250 lb ÷
2
lb
What is the mass in UK
tons, to one decimal place?
1 T (UK) = 2240 lb, so
8250 lb ÷ 2240 lb/T (UK)
2000 lb/T (US)
= 4.125 T (US)
= 3.683... T (UK)
8250 lb is about 4.1 T (US).
8250 lb is about 3.7
T (UK).
Example
Hannah has two bags of nails. Which is heavier, Bag 1 or Bag 2?
Bag 1
650 n1ails
– .
size 1 4 in
1–
mass 2 2
lb
Bag 2
ils
300 na
.
size 3 in
z
o
0
5
s
mas
Solution 1
1
A. How many ounces are in 2 2 lb?
1 lb = 16
oz, so
16
2 lb = 2 ×
oz, or
1
1
lb = × 16
oz, or
2
2
8
oz +
oz =
32
B. Compare.
140
05C05.indd 140
32
50
Apprenticeship and Workplace 10
oz >
40
oz
8
oz
40
oz
oz, so Bag
2
is heavier.
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:29 PM
ReflectiNg
Solution 2
? lb
=
50 oz
A. What is 50 oz in pounds?
?=
1 lb
×
16 oz
50
Why does it not
matter whether
British or
American units
are used for the
nails?
1 lb
16 oz
oz, or 3.125 lb
1
B. Compare. 3.125 lb > 2 2 lb, so Bag
is heavier.
2
Practice
Hint
To see if your
answer is
reasonable, think
about whether the
number of units
should be greater
or less.
1. Express each mass in ounces.
a) a bushel basket of tomatoes, 60 lb
b) a small bag of pet food,
1
32
lb
960
oz
56
oz
2. Express each mass in tons and pounds.
a) 1 cu yd of topsoil, 2400 lb b) 2 cu yd of sand, 5200 lb
=
T (US) 1200 lb,
=
T (US) 400 lb,
2
1
or
1
T (UK)
lb
160
or
T (UK)
2
lb
720
3. What fraction of a pound is each mass?
9
16
a) a small box of plant food, 9 oz
14
16
b) a mini hockey stick, 14 oz
lb
7
lb
or 8
4 lb 6 oz
4. Which backpack is lighter?
e.g., 16 oz = 1 lb, so 21 lb x 16 oz/lb = 8 oz
8 oz > 6 oz, so 4 lb 8 oz > 4 lb 6 oz
The 4 lb 6 oz backpack is lighter.
4 lb 6 oz
5. Chloe is renting a 15 ft box truck to move the contents
3
of her store to a new location. The truck can carry 1 4 T (US).
How many pounds can it carry?
4 12– lb
e.g., 1 T (US) = 2000 lb, so 43 T x 2000 lb/T = 1500 lb
1 43 T (US) = 2000 lb +1500 lb, or 3500 lb
The truck can carry 3500 lb.
4 12– lb
AW10
0-17-650271-8
6. List objects in your classroom that have
a mass of
about 1 lb.
Figure Number
C05-F17-AW10.eps
e.g., a book, an empty backpack
Company
Technical
Pass
Copyright © 2011 by Nelson Education Ltd.
Chapter 5
Hint
Use a scale to help
you.
2nd
Approved
Capacity, Volume, Mass, and Temperature
Not Approved
141
AW10
0-17-650271-8
Figure Number
05C05.indd 141
Company
C05-F17-AW10.eps
4/17/10 12:30:30 PM
5.9
Using Metric Units for Mass
try these
You will need
• balance scales
and masses or a
scale with metric
units (optional)
i) 1 L 
iii) 1 L 
1000 mL
ii) 1 mL  0.001 L
0.001 kL
iv) 1 kg  1000 g
Nick works at a diamond mine north of Yellowknife. Most years,
the mine produces about 8 million carats, which is about 1600 kg
of diamonds. How many metric tonnes is this?
Metric (SI) Units for Mass
ReflectiNg
tonne (t)
Relationship to gram
1 t = 1000 kg, or 103 kg
What patterns
do you see in the
chart?
kilogram (kg)
1 kg = 1000 g, or
103
g
hectogram (hg)
1 hg = 100 g, or
102
g
How is this
chart the same
as the chart for
metric units of
volume? How is it
different?
decagram (dag)
1 dag = 10 g, or
101
g
Which units in the
chart are most
commonly used?
gram (g)
battery,
about 100 g
1
1 dg = 0.1 g, or 10
g
decigram (dg)
centigram (cg)
1 cg = 0.01 g, or
milligram (mg)
1 mg = 0.001 g, or
D
Unit
1
100 g
1
g
1000
raisin,
about 1 g
1
How many tonnes are in 1 kg?
1 t = 1000 kg, so 1 kg = 0.001 t
2
How many tonnes of diamonds are produced a year?
1600 kg × 0.001 t/kg =
1.6 t
AW10
The mass of0-17-650271-8
diamonds is 1.6 t.
Example
Figure Number
C05-F19-AW10.eps
Company
Technical
A bison eats about
6.4 kg of food
a day. What is this in grams?
Pass
1st Pass
Solution 1
1 kg = 1000
Approved
Not Approved
g, so 6.4 kg ×
1000
g/kg = 6400 g
A bison eats about 6400 g of food a day.
142
05C05.indd 142
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:31 PM
ReflectiNg
Solution 2
Which solution
do you prefer,
Solution 1 or
Solution 2? Why?
1000 g
?g
=
6.4 kg
1 kg
?g=
1000 g
× 6.4 kg, or 6400 g
1 kg
A bison eats about 6400 g of food a day.
Practice
1. Express each mass in the units given.
a) a women’s javelin, 600 g
0.6
b) a container of black pepper, 75 g
kg
0.075 kg
c) a sharp-tailed grouse, 0.9 kg
900
g
d) a huge block of ice, 770 kg
0.77
t
e) 15 mg of sodium
0.015 g
f) 5 g of protein
5000 mg
sharp-tailed grouse
(provincial bird
of Saskatchewan)
2. Write each mass using kilograms and grams.
a) a bag of almonds, 1.346 kg
1
kg
346
g
b) a bag of grass seed, 4.75 kg
4
kg
750
g
c) a bag of flour, 2.5 kg
2
kg
500
g
Apprenticeship & Workplace GR 10
3. Some tree planters plant 1600 trees
a day, which is equal to
0-17-650271-8
lifting about 250 kg. How many kilograms
is C05-F20-AW10WB
this in 5 days?
FN
How many tonnes is this in 5 days?
CrowleArt Group
CO
Deborah Crowle
Technical
In 5 days, a tree planter lifts 5 x 250
kg = 1250
kg.
Pass
1000 kg = 1 t, so 1250 kg = 1.250 tApproved
2nd pass
Not Approved
The amount of lifting equals about 1.25 t.
4. Liam conducts whale-watching tours off the
coast of British Columbia. He learned that adult
orcas can have a mass from 2.5 t to 9.0 t. What
are these masses in kilograms?
e.g., 1 t = 1000 kg, so
2.5 t x 1000 kg/t = 2500 kg
9.0 t x 1000 kg/t = 9000 kg
Adult orcas can have a mass from 2500 kg to 9000 kg.
Copyright © 2011 by Nelson Education Ltd.
05C05.indd 143
Chapter 5
Capacity, Volume, Mass, and Temperature
143
4/17/10 12:30:31 PM
AW10.eps
5.10
Mass in Different Systems
try these
Circle the metric units. Underline the imperial (US) units.
You will need
• balance scales
and masses
or a scale with
imperial and
metric units
(optional)
pound
gram
tonne
ounce
ton
A hockey puck has a mass of 6 oz. What is its mass in metric
units?
SI to Imperial (US)
Imperial (US) to SI
∙ 2.21 lb
1 kg =
∙ 0.45 kg
1 lb =
∙ 0.04 oz
1g=
∙ 28.35 g
1 oz =
∙ 0.91 t
1T=
∙ 1.10 T
1t=
ReflectiNg
How can you
express a one-ton
shipment of pucks
in kilograms?
1 T = ? kg
kilogram
1
What is its mass in grams? 1 oz =∙ 28.35 g, so
6 oz × 28.35 g/oz =∙ 170.1 g, or about 170 g
2
What is its mass in kilograms? 1 g = 0.001 kg, so
170 g × 0.001 kg/g =
0.17
kg
Example 1
The greatest mass of Albertosaurus was about 1.9 t. What was its
greatest mass to the nearest tenth of a ton (US)?
Solution 1
A. What relationship will you use? 1 t =∙
1.10
T
B. What is 1.9 t in US tons? 1.9 t × 1.10 T/t =∙
The greatest mass of Albertosaurus was about
ReflectiNg
Should the
number of US
tons be greater
or less than the
number of metric
tonnes? Why?
05C05.indd 144
2.1
T
T.
Solution 2
?T
1.10 T
=∙
1 t
1.9 t
? T =∙
1.10 T
1 t
×
1.9
t, or
2.09
T
The greatest mass of Albertosaurus was about
144
2.09
Apprenticeship and Workplace 10
2.1
T.
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:32 PM
Example 2
Ashley, a fitness coach, calculates body mass index (BMI).
mass in kilograms
height in metres × height in metres
She uses the formula to determine if a person is in the normal
range of 18.5 to 24.9. Is this client within the normal BMI range?
BMI =
Solution
A. What is the client’s mass in kilograms?
1 lb = 0.45 kg, so 120 lb × 0.45 kg/lb =
54.0
kg
B. What is her body mass index?
mass in kilograms
height in metres × height in metres
BMI =
=
=
54.0
1.67 × 1.67
Reflecting
19.362...
C. Is the client within the normal BMI range?
The client’s BMI is 19.4 . This is greater than 18.5 and less
than 24.9 , so her BMI is within the normal range.
Practice
Why do you not
change the units
for the client’s
height?
Note
Use US units in all
of these questions.
1. What can you multiply by to change one unit to the other?
a) tons to tonnes x 0.91
b) pounds to kilograms x 0.45
c) grams to ounces x 0.04
d) kilograms to pounds x 2.21
2. Calculate each mass to the nearest tenth of the metric unit.
a) an empty tractor trailer, 30 000 lb
t
b) a baseball bat, 24 oz 680.4 g
c) a keg of nails, 99 lb
44.6
d) a large polar bear,
3
4
T
0.7
e) the mass that a tool cabinet can hold, 600 lb
270.0
Copyright © 2011 by Nelson Education Ltd.
05C05.indd 145
13.5
kg
t
kg
Chapter 5 Capacity, Volume, Mass, and Temperature
145
4/17/10 12:30:33 PM
AW10.eps
3. Write the correct word below: more or fewer.
1 lb
1 lb
1 kg
a) When you express kilograms as pounds, you will get
more pounds because a pound is less than a kilogram.
b) When you express US tons as metric tonnes, you will get
fewer tonnes because a metric tonne is more than a
US ton.
4. Dani’s tractor is 2200 kg. Express the mass in pounds and in
tons.
a) 1 kg =∙
2.21
lb, so 2200 kg ×
2.21
lb/kg =∙
4862
b) 1 kg = 0.001 t, so 2200 kg × 0.001 t/kg = 2.2
1 t =∙ 1.10 T, so 2.2 t × 1.10 T/t =∙ 2.42 T
lb
t
5. Calculate each mass to the nearest tenth of the imperial unit.
Hint
1 lb = 16 oz.
a) a loaf of bread, 675 g
27.0
oz
b) a sea lion pup, 21 kg
46.4
lb
c) 1 m3 of cement, 1.4 t
1.5
T
d) a box of salt, 1 kg
2.2
lb, or
e) 3 blueberries, 1600 mg
0.1
oz
35.2
oz
6. Pascale is taking a course to learn how to operate heavy
equipment such as a forestry carrier. The mass of a forestry
carrier is 27.9 t. What is its mass in tons?
e.g., 1 t =· 1.10 T, so
27.9 t x 1.10 T/t =· 30.69 T
The mass of the forestry carrier is about 30.7 T.
7. Yvonne bought wool for two of the colours needed to weave
a ceinture fléchée. She bought 200 g of yellow wool from a
store in Brandon, Manitoba, and 8 oz of blue wool during her
trip to the United States. How many more grams of blue wool
did Yvonne buy?
e.g., 1 oz =· 28.35 g
ceinture fléchée
blue wool: 8 oz x 28.35 g/oz =· 226.8 g
226.8 g – 200 g =· 26.8 g
Yvonne bought about 27 g more blue wool.
146
05C05.indd 146
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:34 PM
8. Alex is researching on the Internet before buying a laptop
computer. What is the difference in mass, in kilograms, of
these two computers?
e.g., Mass of 3.31 lb laptop: 3.31 lb x 0.45 kg/lb =· 1.4895 kg
1.86 kg
Difference in mass: 1.86 kg – 1.4895 kg = 0.3705 kg
The difference in mass is about 0.37 kg.
9. How many tonnes can each size of pickup truck carry?
1 T =∙
a) one-ton pickup b) half-ton pickup c) three-quarter-ton pickup
1
2
3
4
3.31 lb
0.91
t
T×
0.91
t/T =∙ 0.46
t
T×
0.91
t/T =∙
t
0.68
10. Hunter is using an online converter. The numbers are 56 and
1.975, but he cannot remember which is ounces and which is
grams. Circle the answer.
56 g and 1.975 oz or 56 oz and 1.975 g
Explain how you know.
e.g., 1 oz =· 28.35 g, so the greater number must be for grams
11. Sujata paid $4.99 for a 10 lb bag of potatoes and $1.49 for a
bag of carrots with a mass of 908 g. What was the cost per
AW10
pound for each bag?
e.g., Cost of potatoes per pound:
0-17-650271-8
Figure Number
C05-F26-AW10.eps
Company
$4.99  10 lb = $0.499/lb
Technical
1st Pass
The mass of the carrots is 0.908 kg.Pass
Approved
1 kg =· 2.21 lb, so 0.908 kg x 2.21 lb/kg =· 2.006 68 lb
Not Approved
Cost of carrots per pound:
$1.49  2.006 68 lb =· $0.742/lb
The potatoes cost about $0.50/lb, and the carrots cost about $0.74/lb.
12. The mass of 1 mL of water is 1 g. What is the mass of 1 L of
water in ounces?
e.g., 1 L has a mass of 1000 g.
1 g =· 0.04 oz, so
1000 g x 0.04 oz/g =· 40 oz
The mass of 1 L of water is about 40 oz.
Copyright © 2011 by Nelson Education Ltd.
05C05.indd 147
Chapter 5 Capacity, Volume, Mass, and Temperature
147
4/17/10 12:30:34 PM
5.11
try these
You will need
Compare. Write >, <, or = to make a true statement.
iii) – 8 > –2 – 8
i) 0 = –1 + 1
• a thermometer
for imperial units
• a thermometer
for metric units
• containers of
water at different
temperatures
(optional)
˚
ii) 6 – 8 > –7
In 1742, Anders Celsius created a Celsius temperature scale. The
metric unit for measuring temperature is degrees Celsius (ºC).
120
40
iv) – 2 + 3 < – 5 + 7
In 1714, Gabriel Daniel Fahrenheit invented the mercury
thermometer. The imperial unit for measuring temperature is
degrees Fahrenheit (°F).
˚
50
The thermometer at the left shows the highest temperature
recorded in Canada. It was on July 5, 1937, in Midale,
Saskatchewan, and Yellow Grass, Saskatchewan.
100
30
80
20
60
10
1
40
0
–10
0
–30
–20
–40
–40
–50
–60
Élise is training to become a chef. A recipe for tourtière says to
bake it at 190 °C. To what temperature should Élise set an oven
with temperatures in degrees Fahrenheit?
Broil
200
550
250
500
450
350
148
05C05.indd 148
400
°F
113
Example 1
B. What is the value of F?
300
ºC or
45
For Celsius and Fahrenheit temperatures, use these formulas:
F = 95 C  32 and C = 59 (F 2 32). F is the temperature in degrees
Fahrenheit and C is the temperature in degrees Celsius.
20
–20
What is the temperature?
Solution
A. Which formula will you use?
-F28-AW10.eps
Pass
temperature in Different Systems
F
F
=
9
5
=
9
5
=
C +32
x 190 +32
374
ºF
C. What temperature for a Fahrenheit oven is closest to the value
you calculated for F? 375 ºF
Élise should set the oven to 375 ºF.
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:35 PM
Example 2
Owen, an assistant at a library, learned that the highest
temperature in Calgary was 36.1 °C on July 25, 1933. The lowest
temperature was 247.9 °F on January 31, 1893. What is the
difference in degrees Celsius, to one decimal place?
Solution
A. Which formula will you use?
C
=
5
9
( F – 32 )
B. What is the value of C?
C
=
5
9
(
–47.9 – 32
)
= –44.388... ºC
C. What is the difference between these temperatures?
36.1 °C 2 ( –44.388... ºC) = 36.1 °C + 44.388... ºC
ReflectiNg
How are the
formulas the
same? How are
they different?
= 80.488... ºC, or about 80.5 °C
˚
120
Practice
100
1. The melting point of ice is 32 ºF.
80
a) Draw an arrow at 32 ºF on the thermometer at the right.
b) What metric temperature equals 32 ºF?
0
ºC
c) Use metric units to write three temperatures at which it
–20 ºC
–25 ºC
would snow. e.g., –10 ºC
d) Use imperial units to write a positive and a negative
temperature at which it would snow.
e.g., 10 ºF
–10 ºF
60
40
20
0
–20
–40
2. Luke and some friends made a snow sculpture for Festival du
Voyageur in Winnipeg. Cross out the temperatures at which
their snow sculpture would start to melt.
6 °C 27 °F 30 °F 23°F 21 °C 12 °F 32 °C 43 °F
3. Express each temperature in degrees Fahrenheit, to the
nearest tenth of a degree if necessary.
a) 22 °C
F =
9
5
b) 0 °C
x (–2) +32
F =
Hint
Circle the formula
you will use:
F = 9 C + 32
9
5
5
C = 5 (F – 32)
9
x 0 +32
AW10
= 28.4 oF
–60
o
= 32
F
0-17-650271-8
Figure Number
C05-F30b-AW10.eps
Company
Technical
Copyright © 2011 by Nelson Education Ltd.
Chapter 5
Pass
2nd Pass
Capacity, Volume, Mass, and Temperature
Approved
149
Not Approved
05C05.indd 149
4/17/10 12:30:36 PM
Hint
Circle the formula
you will use:
F = 9 C + 32
5
C = 5 (F – 32)
9
4. Leah, a weather reporter, uses an online converter to give
temperatures in both Fahrenheit and Celsius. The following
are maximum temperatures on a recent New Year’s Day.
Express each temperature in degrees Celsius, to one decimal
place.
a) 38.5 °F in Victoria, BC
C = 59 (38.5 – 32)
=· 3.6 oC
b) 226.9 °F in Churchill, MB
C = 59 (–26.9 – 32)
=· –32.7 oC
5. Room temperature is often 21 ºC. What temperature should
Kelly select on a thermostat to achieve room temperature to
the nearest degree Fahrenheit?
F =
9
5
x 21 +32
= 69.8 oF
Kelly should select 70 oF.
F
1°
10
6. Jacob knows that normal body temperature is about 37 °C,
but he has a Fahrenheit thermometer from the United States.
Does a body temperature of 101 °F indicate a fever? yes
How do you know?
F =
9
5
x 37 +32
= 98.6 oF
The normal temperature is 98.6 oF, which is lower than 101 oF.
7. Emily is the manager of an arena. She keeps the temperature
of the ice at 16 °F for hockey and 22 °F for figure skating.
Express each temperature in degrees Celsius, to the nearest
degree.
B
a) for hockey
C =
=
5
9
5
9
(F – 32)
(16 – 32)
= – 80
9
·= –9 oC
-F32-AW10.eps
b) for figure skating
C =
=
5
9
5
9
(F – 32)
(22 – 32)
= – 50
9
·= –6 oC
Pass
150
05C05.indd 150
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:36 PM
8. The temperature on the moon can change from 2153 °C
at night to 107 °C during the day. What is the temperature
difference in degrees Fahrenheit?
107 oC – (–153 oC) = 260 oC
F =
=
9
5
9
5
C +32
x 260 +32
= 500 oF
The temperature difference on the moon is 500 oF.
9. Katrina says that 240 °C is about the same as 240 °F.
Do you agree? Explain your thinking.
Yes, e.g., F = 59 C +32
= 59 x (–40) +32
= – 40
10. At sea level, water boils at 100 °C.
a) What is the boiling point of water at sea level, in degrees
Fahrenheit?
F =
=
9
5
9
5
C +32
x 100 +32
= 212 oF
At sea level, water boils at 212 oF.
b) Adam is leading a hike in the Banff National
Park at an altitude of about 1600 m.
The boiling point of water at 1600 m is
202.4 ºF. How does the boiling point of
water change, in degrees Celsius,
from sea level to 1600 m?
212 oF – 202.4 oF = 9.6 oF
The boiling point decreases by 9.6 oF.
A Fahrenheit degree is smaller than
a Celsius degree.
1 oF = 59 oC
9.6 x 59 = 5.333…
The boiling point decreases by 5.3 oC.
Copyright © 2011 by Nelson Education Ltd.
05C05.indd 151
Chapter 5 Capacity, Volume, Mass, and Temperature
151
4/17/10 12:30:36 PM
chapter
Hint
Use the charts
inside the back
cover.
1. Express each capacity in the units given.
1
1
qt =
a) 6 c = 48 fl oz (US) c)
2
32
b) 3 pt = 60 fl oz (UK) d) 4 bu =
pt
gal
2. Ramon works on road construction. He knows that the
asphalt cement and binder must be applied at less than
0.3 gal per square yard. How many quarts of binder are
needed for 8 sq yd of asphalt?
e.g., 8 sq yd x 0.3 gal/sq yd = 2.4 gal
1 gal = 4 qt, so
2.4 gal x 4 qt/gal = 9.6 qt
About 10 qt of binder are needed.
3. Complete. If necessary, round to two decimal places.
a) a fish pond, 6.5 kL
6500
L
b) a jar of mandarin oranges, 540 mL
0.54
L
c) 1 of the 3 bags in a 4 L bag of milk
1.33
L
d) a bottle of baby oil, 592 mL
17.76
fl oz (US)
4. Compare. Write >, <, or = to make a true statement.
a) 1 qt > 1 L
c) 5 mL < 5 fl oz
b) 4 L > 4 pt
d) 3 gal > 3 L
5. Autumn works for a swimming pool company. To determine
the amount of chlorine needed for a pool, she needs to
calculate the capacity in gallons. A pool has a capacity of
25 000 L. What is the capacity in gallons?
e.g., 1 L =· 0.26 gal, so
25 000 L x 0.26 gal/L =· 6 500 gal
The capacity of the pool is about 6500 gal.
6. Express each volume to the nearest whole unit.
a) 2 cu yd =
b) 80 cu ft =·
152
05C05.indd 152
54
3
Apprenticeship and Workplace 10
cu ft
c) 1728 cu in. =
cu yd d) 13 880 cu in. =·
cu ft
1
8
cu ft
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:37 PM
7. Express each volume to the nearest tenth of a unit.
a) 16 cm3 =∙
cu in.
c) 4 cu ft =∙ 113.3 dm3
1.0
b) 4 cu yd =∙
3.0
d) 7 m3 =∙
m3
9.2
cu yd
8. The volume of Nettilling Lake on Baffin Island is 114 km3.
What is the volume of the lake to the nearest cubic mile?
e.g., 1 km3 =· 0.24 cu mi, so
114 km3 x 0.24 cu mi/km3 =· 27.36 cu mi
The volume is about 27 cu mi.
9. Express each mass to the nearest tenth of a unit.
a) a large box of cereal, 700 g
0.7
kg
b) a barge of coal, 21 2 T (US)
19.6
t
c) a container of curry powder, 1.25 oz
35.4
g
d) a capybara, from South America, 75 lb
33.8
kg
1
capybara: the largest
rodent in the world
10. Emma, who is training for a race, read the following on a
soup label: in a 250 mL serving, there are 600 mg potassium
and 23 g carbohydrates.
a) How many grams of potassium are in 250 mL?
e.g., 1 mg = 0.001 g, so
600 mg x 0.001 g/mg = 0.6 g of potassium
b) How many milligrams of carbohydrates are in 250 mL?
e.g., 1 g = 1000 mg, so
23 g x 1000 mg/g = 23 000 mg of carbohydrates
11. Ethan works at a pet store.
He checks
that the GR
water
Apprenticeship
& Workplace
10
temperature for the freshwater
tropical fish is between 76 °F
0-17-650271-8
and 80 °F. What is the lower
in degrees Celsius
C05-F33-AW10WB
FN temperature
to one decimal place? CO
CrowleArt Group
C =
5
9
(76 – 32),
= 24.444..., or 24.4 oC
Technical
Pass
Approved
Not Approved
Hint
F = 9 C + 32
5
C = 5 (F – 32)
9
Deborah Crowle
2nd pass
12. Rachel is a transport refrigeration mechanic. A refrigeration
unit has to be kept at 3 °C. What is that temperature in
degrees Fahrenheit to the nearest degree?
F = 59 x 3 +32,
= 37.4, or 37 oF
Copyright © 2011 by Nelson Education Ltd.
05C05.indd 153
Chapter 5
Capacity, Volume, Mass, and Temperature
153
4/17/10 12:30:37 PM
chapter
Hint
Use the charts
inside the back
cover.
1. Express each capacity in the units given.
a) 9 gal =
72
c) 2004 mL = 2.004 L
pt
b) 56 fl oz (US) =
c d) 4.5 kL = 4500 L
7
2. Jordan picked 7 bu of apples. How many quarts is this?
e.g., 1 bu = 32 qt, so 7 bu x 32 qt/bu = 224 qt
Jordan picked 224 qt of apples.
3. Express each volume in the units given.
a) 10 000 cm3 =
0.01
b) 1000 mm3 =
1
m3 c) 2 cu ft = 3456 cu in.
cm3 d) 8640 cu in. =
5
cu ft
4. Linh rented a storage unit of 500 cu yd for books while she
renovated her store. How many cubic metres did she rent?
e.g., 1 cu yd =· 0.76 m3, so 500 cu yd x 0.76 m3 =· 380 m3
She rented about 380 m3 of storage space.
5. Express each mass to the nearest whole unit.
a) a slice of bread, 25 g
25 000 mg
b) an empty 747 jet, 74 000 kg
74
t
c) a 1 gal can of paint, 7 kg
15
lb
6. The mass of a 1¢ coin is 4.54 g. How many ounces is this?
e.g., 1 g =· 0.04 oz, so
4.54 g x 0.04 oz/g =· 0.1816 oz, or about 0.18 oz
Hint
F = 9 C + 32
5
C = 5 (F – 32)
9
7. Nadia keeps the temperature in a polar bear tank within a degree
of 13 °C. What is this temperature in degrees Fahrenheit?
F =
9
5
x 13 +32
= 55.4 oF
This temperature is about 55 oF.
8. The temperature at Kilauea Volcano in Hawaii reaches
2120 ºF. What is this temperature in degrees Celsius?
C = 59 (2120 – 32)
= 1160 oC
154
05C05.indd 154
This temperature is 1160 oC.
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/17/10 12:30:37 PM