Measurement Conversions

To convert from one unit of measure to another, you multiply by a conversion factor in the form of a fraction. The numerator and denominator are in different units, but they represent the same amount. So you can think of this as multiplying by 1.

An example of a conversion factor is 1  ft 12  in. . fraction 1 ft , over 12 , in. end fraction . .  You can create other conversion factors using the table on page 837.

Example 1

Complete each statement.

1. 88  in . = □  ft 88 , in . equals white square ft

   88  in . ⋅ 1  ft 12  in . = 88 12 ft = 7 1 3 ft 88 , in . dot . fraction 1 ft , over 12 , in . end fraction . equals , 88 over 12 , ft equals 7 , and 1 third , ft

2. 5.3  m = □  cm 5.3 , m equals white square cm

   5.3  m ⋅ 100  cm 1  m = 5.3 ( 100 )  cm = 530  cm 5.3 , m dot . fraction 100 , cm , over 1 m end fraction . equals 5.3 open 100 close cm equals 530 , cm

Area is always in square units, and volume is always in cubic units.

1  yd = 3  ft 1 yd equals 3 ft

1  yd 2 = 9  ft 2 1 yd squared . equals 9 , ft squared

1  yd 3 = 27  ft 3 1 yd cubed . equals . 27 , ft cubed

Example 2

Complete each statement.

1. 300  in . 2 = □  ft 2 300 , in . squared . equals white square , ft squared

   1  ft = 12  in. , so  1   ft 2 = ( 12  in. ) 2 = 144   in. 2 . 300   in. 2 ⋅ 1   ft 2 144   in. 2 = 2 1 12 ft 2 table with 2 rows and 1 column , row1 column 1 , 1 ft equals 12 , in. , comma so 1 , ft squared , equals . open 12 , in. , close squared . equals 144 , in. squared , . , row2 column 1 , 300 , in. squared , dot . fraction 1 , ft squared , over 144 , in. squared end fraction . equals 2 , and 1 twelfth . ft squared , end table

2. 200,000  cm 3 = □  m 3 200,000 . cm cubed . equals white square , m cubed

   1  m = 100  cm , so  1   m 3 = ( 100  cm ) 3 = 1,000,000   cm 3 . 200,000   cm 3 ⋅ 1   m 3 1,000,000   cm 3 = 0.2  m 3 table with 2 rows and 1 column , row1 column 1 , 1 m equals 100 , cm comma so 1 , m cubed , equals . open 100 , cm close cubed . equals . 1,000,000 . , cm cubed , . , row2 column 1 , 200,000 , , cm cubed , dot . fraction 1 , m cubed , over 1,000,000 . , cm cubed end fraction . equals 0.2 , m cubed , end table

Exercises

Complete each statement.

1. 40  cm = □  m 40 , cm equals white square m
2. 1.5  kg = □  g 1.5 , kg equals white square g
3. 60  cm = □  mm 60 , cm equals white square mm
4. 200  in . = □  ft 200 , in . equals white square ft
5. 28  yd = □  in . 28 , yd equals white square in .
6. 1.5  mi = □  ft 1.5 , mi equals white square ft
7. 15  g = □  mg 15 g equals white square mg
8. 430  mg = □  g 430 , mg equals white square g
9. 34  L = □  mL 34 cap l equals white square mcap l
10. 1.2  m = □  cm 1.2 , m equals white square cm
11. 43  mm = □  cm 43 , mm equals white square cm
12. 3600  s = □  min 3600 , s equals white square , min
13. 14  gal = □  qt 14 , gal , equals white square qt
14. 4500  lb = □  t 4500 , lb equals white square t
15. 234  min = □  h 234 , min , equals white square h
16. 3  ft 2 = □  in . 2 3 , ft squared , equals white square in , . squared
17. 108  m 2 = □  cm 2 108 , m squared , equals white square , cm squared
18. 21  cm 2 = □  mm 2 21 , cm squared , equals white square , mm squared
19. 1.4  yd 2 = □  ft 2 1.4 , yd squared , equals white square , ft squared
20. 0.45  km 2 = □  m 2 0.45 . km squared , equals white square , m squared
21. 1300  ft 2 = □  yd 2 1300 . ft squared , equals white square , yd squared
22. 1030  in . 2 = □  ft 2 1030 , in , . squared , equals white square , ft squared
23. 20,000,000  ft 2 = □  mi 2 20,000,000 . ft squared , equals white square , mi squared
24. 1000  cm 3 = □  m 3 1000 . cm cubed , equals white square , m cubed

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