205
7.1 Metric System of Measurement
Introduction
The units of measurement in the metric system are derived from scientific principles. The British
units of measurement, the subsequent US Customary units of measurement and the Imperial
units of measurement are based on different initial standards, stemming from nature and everyday
activities.
Length, weight, capacity (volume), temperature, etc. are measured using several different units of
measurement. The two measurement systems generally in use are the Metric system and the US
Customary system.
The metric system is widely used in science, medicine, technology, and engineering. Most of world
trade utilizes the metric system of measurement. However, the USA and three other countries
(Liberia, Yemen, and Myanmar) have not fully adapted to the metric system.
The metric system for measurement is simple to use and can be more easily understood than the US
Customary system because in the metric system, all the units are related to one another by powers of ten.
Converting within Metric Units of Measurement
The metric system uses metre (m), gram (g), and litre (L) as the base units for the measurements of
length, mass, and capacity, respectively. The Celsius (°C) scale is used for temperature.
In this section, you will learn how to convert the commonly used units for length, mass, and capacity within
the following metric units:
■■ Length: kilometre (km), metre (m), centimetre (cm), and millimetre (mm)
■■ Mass: kilogram (kg), gram (g), and milligram (mg)
■■ Capacity: litre (L) and millilitre (mL)
The conversion factors that relate to the different units in the metric system, including the prefixes
used, are shown in Table 7.1.
Table 7.1
The prefix and symbol for
units from kilo- to milliare written in lower case.
The Base Unit is
metre (for length),
gram (for mass), and
litre (for capacity).
The prefixes hecto-, deca-,
and deci-units are usually
not used as units of
measurement for length,
mass, and capacity. The
prefix centi- is used only
in the measurement of
length, as in centimetre.
Conversion Factors
Prefix
Symbol
Factor
Factor in Word
Factor in
Powers of 10
kilo-
k
1,000
Thousand
103
hecto-
h
100
Hundred
102
deca-
da
10
Ten
101
Base Unit
1
One-tenth
10–1
= 0.01
One-hundredth
10–2
= 0.001
One-thousandth
10–3
deci-
d
centi-
c
milli-
m
1
10
1
100
1
1,000
= 0.1
Converting units within the metric system involves moving the decimal point to the right or to
the left, by the appropriate number of places (which is the same as multiplying or dividing by the
required powers of 10).
7.1 Metric System of Measurement
206
The conversion within the units of measurement can also be shown in a horizontal line diagram, in
order from the largest to the smallest.
×10
kilo -
×10
hecto -
÷10
×10
×10
Base Unit
deca -
÷10
×10
÷10
×10
deci -
÷10
centi -
÷10
milli -
÷10
The conversion from a larger unit to a smaller unit represents moving the decimal point to the right
or multiplying by powers of 10 as required.
For example, to convert 10.5 kilometres (km) to metres (m), move the decimal point 3 places to the
right or multiply by 103 (or 1,000).
3 places to the right
km
m
10.5 km = 10.5 . m
= 10,500 m
cm
mm
10.5 km = 10.5 × 103 m
or
= 10.5 × 1,000 m
= 10,500 m
The conversion from a smaller unit to a larger unit represents moving the decimal point to the left or
dividing by powers of 10 as required.
For example, to convert 425 centimetres (cm) to metres (m), move the decimal point 2 places to the
left or divide by 102 (or 100).
km
m
cm
mm
2 places to the left
425 cm =
425 cm = 4.25 m
= 4.25 m
or
=
425
425
100
10
2
m
m
= 4.25 m
Length
Converting from larger units to smaller units
Chapter 7 | Units of Measurement
Converting from smaller units to larger units
 1 
 km = 0.001 km
 1,000 
1 km = (1 × 1,000) m = 1,000 m
1m=
1 m = (1 × 100) cm = 100 cm
1 cm = 
1 cm = (1 × 10) mm = 10 mm
1 mm = 
 1 
 m = 0.01 m
 100 
1
 cm = 0.1 cm
 10 
207
Mass
Converting from larger units to smaller units
1 metric ton or metric
tonne (t) = 1,000 kg
Converting from smaller units to larger units
 1 
 kg = 0.001 kg
 1,000 
1 kg = (1 × 1,000) g = 1,000 g
1g=
 1 
 g = 0.001 g
 1,000 
1 g = (1 × 1,000) mg = 1,000 mg
The capitalized ‘L’ is
used to represent litre in
order to avoid confusion
with the number 1.
Capacity
Converting from larger units to smaller units
Converting from smaller units to larger units
 1 
 L = 0.001 L
 1,000 
1 L = (1 × 1,000) mL = 1,000 mL
1 cubic metre or metre
cube (m3) = 1,000 L
Example 7.1-a
1 mg = 
1 mL = 
Converting Measurements
Convert the following measurements:
(i)
7.5 cm to millimetres
(ii)
(iii) 2.56 kg to grams
Solution
(i)
(ii)
1,120 cm to metres
(iv) 21,750 mL to litres
7.5 cm to millimetres:
7.5 cm = 7.5 × 10 mm = 75 mm
(same as 7.5 = 75 mm)
1,120 cm to metres:
1,120
1,120 cm =
m = 11.2 m
100
1 place to the right
× 10
km
m
cm
mm
km
m
cm
mm
÷ 10
÷ 10
2 places to the left
(same as 1,120 = 11.2 m)
(iii) 2.56 kg to grams:
2.56 kg = 2.56 × 1,000 g = 2,560 g
(same as 256 . = 2,560 g)
(iv) 21,750 mL to litres:
21,750
21,750 mL =
L = 21.75 L
1,000
3 places to the right
× 10
× 10
× 10
kg
g
mg
kL
L
mL
÷ 10
÷ 10
÷ 10
3 places to the left
(same as 21,750 = 21.75 L)
Example 7.1-b
Converting Measurements in Multiple Units
Convert the following measurements:
(i)
Solution
(i)
12 m 25 cm to centimetres
(ii) 2 kg 456 g to grams
(iii) 3 L 75 mL to millilitres
12 m 25 cm to centimetres:
12 m 25 cm = 12 m + 25 cm
= (12 × 100) cm + 25 cm
= 1,200 cm + 25 cm
= 1,225 cm
Therefore, 12 m 25 cm is equal to 1,225 cm.
7.1 Metric System of Measurement
208
Solution
(ii)
continued
2 kg 456 g to grams:
2 kg 456 g = 2 kg + 456 g
= (2 × 1,000) g + 456 g
= 2,000 g + 456 g
= 2,456 g
Therefore, 2 kg 456 g is equal to 2,456 g.
(iii) 3 L 75 mL to millilitres:
3 L 75 mL = 3 L + 75 mL
= (3 × 1,000) mL + 75 mL
= 3,000 mL + 75 mL
= 3,075 mL
Therefore, 3 L 75 mL is equal to 3,075 mL.
Example 7.1-c
Converting Measurements and Expressing in Multiple Units
Convert the following measurements:
(i)
Solution
695 cm to metres and centimetres
(i) 695 cm to metres and centimetres:
Method 1:
 695 
 m = 6.95 m
 100 
695 cm = 
= 6 m + 0.95 m
= 6 m + (0.95 × 100) cm
(ii) 2,275 mL to litres and millilitres
Method 2:
695 cm = 600 cm + 95 cm
 600 
 m + 95 cm
 100 
= 
= 6 m 95 cm
= 6 m + 95 cm
= 6 m 95 cm
Therefore, 695 cm is equal to 6 m 95 cm.
(ii) 2,275 mL to litres and millilitres:
Method 1:
 2,275 
 L = 2.275 L
 1,000 
2,275 mL = 
= 2 L + 0.275 L
= 2 L + (0.275 × 1,000) mL
Method 2:
2,275 mL = 2,000 mL + 275 mL
= 
2,000 
 L + 275 mL
 1,000 
= 2 L 275 mL
= 2 L + 275 mL
= 2 L 275 mL
Therefore, 2,275 mL is equal to 2 L 275 mL.
Example 7.1-d
Converting Measurements Involving Two Steps
Convert the following measurements:
(i)
Chapter 7 | Units of Measurement
5 km 20 m to centimetres
(ii)
3,125,000 mg to kilograms and grams
209
Solution
(i)
5 km 20 m to centimetres:
Method 1:
Method 2:
Step 1: Convert 5 km 20 m to metres,
5 km 20 m = 5 km + 20 m
= (5 × 105) cm + (20 × 102) cm
= (5 × 1,000) m + 20 m
= 500,000 cm + 2,000 cm
= 5,000 m + 20 m
= 502,000 cm
5 km 20 m = 5 km + 20 m
= 5,020 m
Step 2: Convert 5,020 m to centimetres,
5,020 m = (5,020 × 100) cm
= 502,000 cm
Therefore, 5 km 20 m is equal to 502,000 cm.
(ii)
3,125,000 mg to kilograms and grams:
Method 1:
Method 2:
Step 1: Convert 3,125,000 mg to grams
 3,125, 000 
 kg
6
 10

3,125,000 mg = 
 3,125, 000 
g
 1, 000 
3,125,000 mg = 
= 3,125 g
Step 2: Convert 3,125 g to kilograms and grams
 3,125 
 kg
 1,000 
3,125 g = 
= 3.125 kg
= 3 kg + 0.125 kg
= 3 kg + (0.125 × 1,000) g
= 3 kg + 125 g
= 3 kg 125 g
= 3.125 kg
= 3 kg + 0.125 kg
= 3 kg + (0.125 × 103) g
= 3 kg + 125 g
= 3 kg 125 g
Therefore, 3,125,000 mg is equal to 3 kg 125 g.
Example 7.1-e
Word Problems Involving Conversion of Measurements
Megan bought 1.5 kg of flour and used 925 g of it. Calculate the quantity of flour remaining, in grams.
Solution
Since the answer needs to be expressed in grams, convert all measurements into grams.
1.5 kg = (1.5 × 1,000) g [using 1 kg = 1,000 g]
= 1,500 g
As she used 925 g of flour, this needs to be subtracted from the total.
Remaining flour = (1,500 – 925) g
= 575 g
Therefore, the quantity of flour remaining is 575 g.
7.1 Metric System of Measurement
210
7.1 Exercises
Answers to odd-numbered problems are available at the end of the textbook.
Calculate the missing values in Problems 1 to 8.
1.
2.
metres (m)
centimetres (cm)
millimetres (mm)
metres (m)
centimetres (cm)
millimetres (mm)
a.
2.40
?
?
a.
1.20
?
?
b.
?
860
?
b.
?
975
?
c.
?
?
34,420
c.
?
?
23,170
metres (m)
centimetres (cm)
millimetres (mm)
metres (m)
centimetres (cm)
millimetres (mm)
a.
0.25
?
?
a.
0.67
?
?
b.
?
58
?
b.
?
95
?
c.
?
?
8,470
c.
?
?
5,200
kilometres (km)
metres (m)
centimetres (cm)
kilometres (km)
metres (m)
centimetres (cm)
a.
1.62
?
?
a.
1.25
?
?
b.
?
2,390
?
b.
?
1,454
?
c.
?
?
2,320
c.
?
?
1,190
kilometres (km)
metres (m)
centimetres (cm)
kilometres (km)
metres (m)
centimetres (cm)
a.
0.65
?
?
a.
0.17
?
?
b.
?
154
?
b.
?
230
?
c.
?
?
1,770
c.
?
?
9,400
3.
5.
7.
4.
6.
8.
For Problems 9 to 12, convert the measurements to the units indicated.
9. a. 23 m 21 cm = ___ cm
b. 16 cm 7 mm = ___ mm
c. 5 km 252 m = ___ m
10. a. 7 m 49 cm = ___ cm
b. 45 cm 8 mm = ___ mm
c. 2 km 725 m = ___ m
11. a. 335 cm = ___ m ___ cm
b. 603 mm = ___ cm ___ mm
c. 1,487 m = ___ km ___ m
12. a. 793 cm = ___ m ___ cm
b. 379 mm = ___ cm ___ mm
c. 6,745 m = ___ km ___ m
13. Arrange the following measurements in order from smallest to largest:
0.15 km, 150,800 mm, 155 m, 15,200 cm
14. Arrange the following measurements in order from largest to smallest:
19,750 cm, 1.97 km, 1,950 m, 195,700 mm
15. The distance between my house and the office is 1.7 km. I walked 925 m. How many more metres would I have to
walk to reach the office?
16. In a 2.5 km race, there is a checkpoint at 875 m from the finish line. Calculate the distance, in metres, that I would
have to run to reach the checkpoint.
17. Ali is 1.75 m tall. Eric is 30 mm taller than Ali. Calculate Eric’s height, in centimetres.
18. Five-year-old Aran is 1.2 m tall. His sister, Girija, is 40 mm taller than him. Calculate Girija’s height, in centimetres.
Calculate the missing values in Problems 19 to 26.
19.
kilograms (kg)
grams (g)
a.
2.62
?
b.
?
6,750
kilograms (kg)
grams (g)
a.
0.84
?
b.
?
580
21.
Chapter 7 | Units of Measurement
20.
kilograms (kg)
grams (g)
a.
3.79
?
b.
?
8,620
kilograms (kg)
grams (g)
a.
0.32
?
b.
?
930
22.
211
23.
kilograms (kg)
grams (g)
milligrams (mg)
a.
1.65
?
?
b.
?
4,950
?
c.
?
?
6,440
kilograms (kg)
grams (g)
milligrams (mg)
a.
2.45
?
?
b.
?
8,700
?
c.
?
?
3,890
kilograms (kg)
grams (g)
milligrams (mg)
a.
0.76
?
?
b.
?
35,760
?
c.
?
?
50,300
kilograms (kg)
grams (g)
milligrams (mg)
a.
0.45
?
?
b.
?
25,090
?
c.
?
?
20,080
24.
25.
26.
For Problems 27 to 30, convert the measurements to the units indicated.
27. a. 18 kg 79 g = ___ g
b. 2 kg 116 mg = ___ mg
c. 3 t 74 kg = ___ kg
28. a. 7 kg 89 g = ___ g
b. 14 kg 547 mg = ___ mg
c. 15 t 90 kg = ___ kg
29. a. 5,903 g = ___ kg ___ g
b. 2,884 mg = ___ g ___ mg
c. 9,704 kg = ___ t ___ kg
30. a. 5,014 g = ___ kg ___ g
b. 6,629 mg = ___ g ___ mg
c. 3,075 kg = ___ t ___ kg
31. Arrange the following measurements in order from smallest to largest:
0.075 t, 123,200 g, 850,250 mg, 125 kg
32. Arrange the following measurements in order from largest to smallest:
0.025 t, 50,750 mg, 125,700 g, 27 kg
33. If one tablespoon of salt weighs 5.5 g, how many tablespoons of salt are there in a box containing 1.1 kg of salt?
34. If a bowl can hold 40 g of cereal, how many bowls of cereal will you obtain from a box that has 1.35 kg of cereal?
35. Linda is baking a cake. She bought 0.75 kg of sugar and used 575 g of it. Calculate the quantity of sugar left, in grams.
36. Ben bought 1.3 kg of meat and cooked 650 g of it for dinner. Calculate the quantity of meat left, in grams.
37. 450 g of butter cost $3.25. At this price, how much will it cost to buy 2.25 kg of butter?
38. 250 g of cheese cost $2.75. At this price, how much will it cost to buy 2 kg of cheese?
Calculate the missing values in Problems 39 to 42.
39.
litre (L)
millilitre (mL)
a.
3.25
?
b.
?
5,060
litre (L)
millilitre (mL)
a.
0.045
?
b.
?
220
41.
40.
litre (L)
millilitre (mL)
a.
1.75
?
b.
?
1,975
litre (L)
millilitre (mL)
a.
0.015
?
b.
?
5,730
42.
7.1 Metric System of Measurement
212
For Problems 43 to 46, convert the measurements to the units indicated.
43. a. 5 L 85 mL = ___ L
b. 2 L 5 mL = ___ L
44. a. 9 L 25 mL = ___ L
b. 1 L 205 mL = ___ L
45. a. 2,708 mL = ___ L ___ mL
b. 12,080 mL = ___ L ___ mL
46. a. 6,503 mL = ___ L ___ mL
b. 32,096 mL = ___ L ___ mL
47. A bottle can hold 900 mL of orange juice. Calculate the total volume of orange juice in five bottles. Express the answer
in litres.
48. Andy drinks 250 mL of milk every day. Calculate the quantity of milk he will require for 7 days. Express the answer
in litres.
49. A milk carton contains 1.75 L of milk. If three glasses with a volume of 320, mL, each are filled with milk from the
packet, how much milk will be left in the carton? Express the answer in millilitres.
50. A bottle can hold 1.5 L of wine. If four glasses with a volume of 280 mL, each, are filled with wine from the bottle,
how much wine will be left in the bottle? Express the answer in millilitres.
7.2 US Customary System of Measurement
In the United States, units in the US Customary system are primarily used for the purposes of
measurements. Imperial units of measurement were historically used in the British Commonwealth
countries.
While the Imperial and US Customary systems are very similar, they are not identical. There are a
number of differences between them.
For example,
•
The imperial ton is 2,240 pounds, whereas the US ton is 2,000 pounds. (1 U.S. ton = 0.893
Imperial ton)
•
The imperial gallon is the volume of 10 pounds of water, whereas the US gallon is the volume
of 81/3 pounds of water. (1 U.S. gallon = 0.833 Imperial gallons)
The US Customary system uses the yard (yd), the pound (lb), and the gallon (gal) as the base units
for the measurements of length, mass, and capacity, respectively. The Fahrenheit (°F) scale is used
for temperature.
In the United States, many items are measured using US Customary units. For example, road distance
is measured in miles, butter is measured in pounds, and gasoline is measured in gallons.
The base unit is yard (for
length), pound (for mass),
and gallon (for capacity).
In this section, you will learn how to convert within the commonly used units for length, mass, and
capacity within the following US Customary units:
■■ Length: mile (mi), yard (yd), foot (ft), and inch (in)
■■ Mass: ton (ton), pound (lb), and ounce (oz)
■■ Capacity: gallon (gal), quart (qt), pint (pt), cups (c), and fluid ounce (fl oz)
Converting within US Customary Units of Measurements
Length
Chapter 7 | Units of Measurement
■■ 1 mile is 1,760 yd or 5,280 feet
1 mi = 1,760 yd = 5,280 ft
■■ 1 yard is 3 feet
1 yd = 3 ft
■■ 1 foot is 12 inches
1 ft = 12 in