ACT Math study guide · Chapter 39
Measurement and Unit Conversion
Converting a linear measurement multiplies or divides by the conversion factor once. Converting a square measurement (area) requires squaring that factor, since area scales in two dimensions. Converting a cubic measurement (volume) requires cubing it, since volume scales in three dimensions. Applying only the linear factor to a square or cubic conversion is one of the most common errors on this topic.
A compound rate, like miles per hour converted to feet per second, changes two units at once. Converting the distance unit and the time unit separately, then combining both conversions, keeps the process organized and avoids dropping a factor along the way.
Where this appears as a model: a coverage rate applied to a real space. A paint that covers 350 square feet per gallon requires 4 gallons to cover a 1,400-square-foot room, found by dividing the total area by the coverage rate.
▸ Squared and cubed unit conversions
Worked Example Convert 3 square feet to square inches.
Square the linear conversion factor for an area conversion.
1 square foot = 12² = 144 square inches
3 × 144 = 432
▸ Compound rate conversions
Worked Example Convert 30 miles per hour to feet per second.
Convert the distance and time units separately, then combine them.
30 × 5,280 ÷ 3,600 = 44
▸ Practice
Question 1
- AA. 8
- BB. 96
- CC. 24
- DD. 2.67
Question 2
- FF. 72
- GG. 2592
- HH. 1296
- JJ. 5184
Question 3
- AA. 6912
- BB. 48
- CC. 576
- DD. 1728
Question 4
- FF. 60
- GG. 66
- HH. 72
- JJ. 45
Question 5
- AA. 100
- BB. 1,000
- CC. 100,000
- DD. 10,000
Question 6
- FF. 125
- GG. 175
- HH. 100
- JJ. 150
Question 7
- AA. 18
- BB. 72
- CC. 90
- DD. 108
Question 8
- FF. 54
- GG. 18
- HH. 24
- JJ. 36
Question 9
- AA. 36
- BB. 108
- CC. 12
- DD. 324
Question 10
- FF. 60
- GG. 44
- HH. 88
- JJ. 52.8
Question 11
- AA. 225
- BB. 255
- CC. 240
- DD. 250
Question 12
- FF. 75
- GG. 750
- HH. 7.5
- JJ. 0.75
Question 13
- AA. 3,168
- BB. 9,240
- CC. 5,280
- DD. 1,760
Question 14
- FF. 3,600
- GG. 1,200
- HH. 600
- JJ. 900
Question 15
- AA. 33
- BB. 30
- CC. 36
- DD. 27
Question 16
- FF. 72
- GG. 720
- HH. 864
- JJ. 648
Question 17
- AA. 150
- BB. 165
- CC. 175
- DD. 160
Question 18
- FF. 22
- GG. 44
- HH. 66
- JJ. 30
Question 19
- AA. 12
- BB. 120
- CC. 1,200
- DD. 1.2
Question 20
- FF. 7,040
- GG. 5,280
- HH. 12
- JJ. 1,760
▸ Answers and Explanations
Show the answers and explanations
1: C. 8 yards × 3 feet/yard = 24 feet. Choice A reports the original value in yards, forgetting to convert to feet at all.
2: G. 1 square yard = 36² = 1,296 square inches; 2 × 1,296 = 2,592. Choice F uses the linear conversion factor (36) instead of squaring it for a square-unit conversion.
3: A. 1 cubic foot = 12³ = 1,728 cubic inches; 4 × 1,728 = 6,912. Choice B uses the linear conversion factor (12) instead of cubing it for a cubic-unit conversion.
4: G. 45 × 5,280 ÷ 3,600 = 66 feet per second. Choice F comes from an arithmetic slip while combining the conversion factors for distance and time.
5: D. 1 kilogram = 1,000 grams; 10 × 1,000 = 10,000. Choice A uses an incorrect conversion factor instead of the 1,000 grams per kilogram relationship.
6: J. 2.5 × 60 = 150 minutes. Choice F comes from an arithmetic slip while multiplying 2.5 by 60.
7: D. 9×12=108 inches. Choice A divides by 12 instead of multiplying, reversing the conversion direction.
8: F. 1 square yard=9 square feet; 6×9=54. Choice G uses the linear conversion factor (3) instead of squaring it for a square-unit conversion.
9: B. 1 cubic yard=27 cubic feet; 4×27=108. Choice A uses the linear conversion factor (3) instead of cubing it for a cubic-unit conversion.
10: F. 88×3,600÷5,280=60 miles per hour. Choice G comes from an arithmetic slip while combining the conversion factors for distance and time.
11: B. 4.25×60=255 minutes. Choice A comes from an arithmetic slip while multiplying 4.25 by 60.
12: H. 1,000 grams=1 kilogram; 7,500÷1,000=7.5. Choice F divides by 100 instead of 1,000, a factor-of-10 error.
13: C. 1 mile=1,760 yards; 3×1,760=5,280. Choice A comes from an arithmetic slip while multiplying 3 by 1,760.
14: G. 20×60=1,200 seconds. Choice F uses the conversion factor for an hour instead of a minute, multiplying by 60×60 instead of 60.
15: A. 11×3=33 feet. Choice B comes from an arithmetic slip while multiplying 11 by 3.
16: H. 1 square foot=144 square inches; 6×144=864. Choice J comes from an arithmetic slip while multiplying 6 by 144.
17: B. 2.75×60=165 minutes. Choice A comes from an arithmetic slip while multiplying 2.75 by 60.
18: J. 44×3,600÷5,280=30 miles per hour. Choice F comes from an arithmetic slip while combining the conversion factors for distance and time.
19: A. 1,000 grams=1 kilogram; 12,000÷1,000=12. Choice B divides by 100 instead of 1,000, a factor-of-10 error.
20: F. 1 mile=1,760 yards; 4×1,760=7,040. Choice G reports the conversion factor for a single mile instead of multiplying by the requested 4 miles.