Section 5-1: The U.S. Customary System of Measurement
Learning Outcome 1
Identify a reasonable U.S. customary measure for the following:
mi
Cough syrup, oz; woman, lb; elephant, T; speed limit sign,
; photograph, in.; entry door, ft;
hr
carpet, yd; milk, qt; paint, gal; flour, c
Learning Outcome 2
Convert 3 gal to pt using unity ratios.
3 gal
1
·
4 qt
1 gal
·
2 pt
= 24 pt
1 qt
Multiply by unity ratios that change gal to qt and qt to pt.
Cancel like units of measure.
Convert 3 1 ft to in. using a unity ratio.
4
1
13
3 ft =
ft
4
4
3
13 ft 12 in.
·
= 39 in.
4
1 ft
1
Multiply by a unity ratio to change ft to in.
Cancel like units of measure. Reduce numerator and
denominator that have a common factor.
Convert 10 qt to gal using unity ratios.
5
10 qt
1
·
1 gal 5 gal
1
=
= 2 gal
2
4 qt
4 qt
2
Multiply by a unity ratio to change qt to gal.
Cancel like units of measure. Reduce numerator and
denominator that have a common factor.
Learning Outcome 3
Convert 48 in. to yd using a conversion factor.
1 yd = 36 in.
in. ·
yd
= yd
in.
1 yd
= 0.0278 conversion factor
36 in.
48 in. · 0.0278 = 1.3 yd (rounded)
Learning Outcome 4
4 yd 8 ft = 6yd 2 ft
Standard notation
8 ft = 2 yd 2 ft (8 ft ÷ 3 ft = 2 yd 2 ft)
Section 5-2: Adding and Subtracting U.S. Customary Measures
Learning Outcome 1
Add 2 qt and 6 oz.
2 qt 32 oz
·
= 64 oz
1
1 qt
64 oz + 6 oz = 70 oz
Convert qt to oz.
Add like measures.
Learning Outcome 2
Subtract 2 yd 2 ft from 4 yd.
3 yd 3 ft
-2 yd 2 ft
Rewrite 4 yd as 3 yd 3 ft.
Subtract like measures.
1 yd 1 ft
Section 5-3: Multiplying and Dividing U.S. Customary Measures
Learning Outcome 1
Multiply 2 lb 7 oz by 3.
2 lb 7 oz
x
3
6 lb 21 oz = 7 lb 5oz
Learning Outcome 2
Multiply 4 ft by 3 ft.
4 ft x 3 ft = 12ft2
Multiply each measure by 3. Write product in standard notation.
21 oz = 1 lb 5 oz.
The product is square measure.
Learning Outcome 3
Divide 5 gal 3 qt by 3.
2
1 gal 3 qt
3
3 5 gal 3 qt
)
3 gal
= 8 qt
2 gal
11 qt
9 qt
Divide 3 into 5 gal.
1 gal x divisor 3 = 3. Subtract 3 gal from 5 gal.
Convert gallons to quarts. Add 3 qt + 8 qt = 11 qt.
11 qt ÷ divisor 3 = 3 qt. 3 qt x divisor 3 = 9 qt.
11 qt – 9 qt = 2 qt.
2
Write the remainder as a fraction, 3 , to represent 2 qt ÷ divisor
3.
2 qt
Learning Outcome 4
How many 8-oz glasses of milk can be poured from 1 gallon of milk?
1 gal ·
4 qt
1 gal
·
2 pt
1 qt
·
2 c 8 oz
·
1 pt 1 c
1 gal ÷ 8 oz
128 oz ÷ 8 oz = 16 8-oz glasses
Learning Outcome 5
The speed limit in a school zone is 20 miles per hour. This is the same as how many feet per
second?
1
ft
20 mi 5, 280 ft
1 hr
1 min 5, 280 ft
= 29.3
·
·
·
=
sec
hr
1 mi
60 min 60 sec 180 sec
3
Section 5-4: Introduction to the Metric System
Learning Outcome 1
Identify a reasonable metric measure for the following:
Nasal spray, mL; root beer, L; distance between cities, km; relay race, m; aspirin, mg; sack of
corn, kg; sugar cube, g.
Learning Outcome 2
Convert 3.6 m to centimeters. To change to a smaller unit, move decimal to the right the number
of places the new unit is from the original unit on the chart.
3.6 m = 360 cm
On the chart, cm is two places to right of m.
Convert 3,897 L to kiloliters. To change to a larger unit, move decimal to the left the number of
places the new unit is from the original unit on the chart.
3,897 L = 3.897 kL
On the chart, kL three places to the left of L.
Learning Outcome 3
5 cm + 4 dm
5 cm + 40 cm = 45 cm
or
0.5 dm + 4 dm = 4.5 dm
Change to a common unit of measure and add.
4 dm = 40 cm.
5 cm = 0.5 dm.
12.6 cm x 3 = 37.8 cm
Multiply and keep the unit of measure.
352 km ÷ 5 km
Divide. The units of measure cancel.
352 km
= 70.4
5 km
Section 5-5: Metric-U.S. Customary Comparisons
Learning Outcome 1
How many inches are in 24 cm?
24 cm
1 in.
·
= 9.45 in.
1
2.54 cm
Use conversion relationship 1 in. = 2.54 cm. Other relationships
can be used.
How many kilometers are in 3.6 mi?
3.6 mi 1.61 km
·
= 5.796 km
1
1 mi
Use conversion relationship 1 mi = 1.61 km. Other relationships
can be used.
Section 5-6: Time
Learning Outcome 1
How many hours are in 5 days?
5 days
1
·
24 hr
= 120 hr
1 day
Learning Outcome 2
It takes a laser engraver 1 min 12 sec to engrave a certain logo. How long will it take to engrave
25 logos?
1 min 12 sec
·
25
60
24
5
300 sec
1 min
·
= 5 min
1
60 sec
1
25 min 300 sec
25 min + 5 min = 30 min
Learning Outcome 3
If it is 5 p.m. in Salt Lake City Utah (–7 GMT), what time is it in Charleston, South Carolina (–5
GMT)?
–5 – (–7) = –5 + 7 = +2
two hours later
5 p.m. + 2 hr = 7 p.m.
Section 5-7: Reading Instruments Used to Measure Length
Learning Outcome 1
How many significant digits are in the numbers 280,300 and 0.0103?
280,300 has 4 significant digits.
0.0103 has 3 significant digits.
Learning Outcome 2
5
What is the precision and greatest possible error of a measurement of 3
in.?
16
1
The precision is
in.
16
1 1
1
=
in.
The greatest possible error is one-half the precision or
2 Ł16 ł 32
Learning Outcome 3
Learning Outcome 4
Learning Outcome 5
Find the midpoint and distance between the points 2.7 cm and 8.2 cm.
Distance: 8.2 - 2.7 = 5.5 cm
2.7 + 8.2 10.9
Midpoint:
=
= 5.45 cm
2
2
Section 5-8: Temperature Formulas
Learning Outcome 1
Use the formula K=ºC + 273 to change 25ºC to K.
K = ºC + 273
Substitute 25 in place of ºC.
K = 25 + 273
Simplify.
K = 298
Use the formula ºC = K –273 to change 425 K to ºC.
ºC = K – 273
Substitue 425 in place of K.
ºC = K – 273
Simplify.
ºC = 152
Lesson Outcome 2
Use the formula °R = °F + 460 to change 72°F to °R.
°R = °F + 460
Substitute 72 in place of °F.
°R = 72 + 460
Simplify.
°R = 532
Use the formula °F = °R – 460 to change 182°R to °F.
°F = °R – 460
Substitute 182 in place of °R.
°F = 182 – 460
Simplify.
°F = –278
Lesson Outcome 3
5
Use the formula °C =
(°F − 32) to find the Celsius temperature for 95 degrees Fahrenheit.
9
5
(°F − 32)
9
5
°C =
(95 − 32)
9
5
°C =
(63)
9
°C = 35°
°C =
Substitute 95 for °F.
Simplify grouping.
Perform multiplication.
Lesson Outcome 4
9
Use the formula °F =
°C + 32 to determine the number of Fahrenheit degrees in 0 degrees
5
Celsius.
9
°C + 32
5
9
°F =
(0) + 32
5
°F = 0 + 32
°F = 32
°F =
Substitute known value for equivalent unknown letter.
Perform order of operations (multiply first).
Simplify.