56 CHAPTER 2
Arithmetic
2.2 INTERCHANGING FRACTIONS, DECIMALS, AND PERCENTS
Textbook Reference Section 5.3
CLAST OBJECTIVE
" Identify equivalent forms of decimals, percents, and fractions
Rule 1: Fraction to Percent
To change a fraction to a percent, multiply the fraction by 100.
Rule 2: Fraction to Decimal
To change a fraction to a decimal, divide the numerator by the denominator.
Examples
3
a) Write as a percent.
8
Solutions
3 10025
3
× 100 = ×
8 1
8
2
=
b) Write
3
as a decimal.
8
3 × 25 75
1
=
= 37 % or 37.5%
2 ×1
2
2
0.375
8 3.000
24
60
56
40
40
0
Rule 3: Decimal to Percent
To change a percent to decimal, move the decimal point two places to the right.
Rule 4: Decimal to Fraction
To change a decimal to a fraction, remove the decimal point and place the number
over 10 or 100 or 1000, etc. The number of zeroes is equal to the number of digits
to the right of the decimal point in the original number.
Examples
c) Write 5.43 as a percent.
Solutions
Move decimal two places to the right and add
a percent sign: 5.43 = 543. = 543 %
d) Write 5.43 as a fraction.
Note that there are two digits to the right of
the decimal point. We will drop the decimal
point and place the number over 100.
543
43
=5
100
100
© Houghton Mifflin Company. All rights reserved.
SECTION 2.2
Interchanging Fractions, Decimals, and Percents 57
Rule 5: Percent to Decimal
To change a percent to decimal, drop the percent sign and move the decimal point
two places to the left.
Rule 6: Percent to Fraction
To change a percent to a fraction, drop the percent sign and write the number over
100 and reduce, if possible.
Examples
Solutions
e) Write 71 % as a decimal.
71 % = 0.71
71 % =
f) Write 71 % as a fraction.
Check Your Progress 2.2
3
1. Change to a percent.
4
3. Write
5
as a decimal.
8
2. Change 6
4. Write 9
71
100
1
to a percent.
5
2
as a decimal.
5
5. Write 0.732 as a percent.
6. Write 1.3 as a percent.
7. Change 0.89 to a fraction.
8. Change 12.4 to a fraction.
9. Change 47 % to decimal.
10. Change 319 % to decimal.
11. Change 52 % to fraction.
12. Change 150 % to fraction.
© Houghton Mifflin Company. All rights reserved.
58 CHAPTER 2
Arithmetic
See If You
Remember
SECTION 2.1
1. 3.25 + 161.9 + 22.831
2. 20.4 – 9.005
3. 0.57 • 6.21
4. 14.4 ÷ 0.024
1 ⎛
3⎞
5. − 1 + ⎜ − 4 ⎟
3 ⎝
7⎠
3 ⎛
4⎞
6. 2 − ⎜ − 2 ⎟
5 ⎝
9⎠
2 3
7. − 2 ×
7 4
8. −
1 ⎛ 2⎞
÷ ⎜− ⎟
5 ⎝ 9⎠
© Houghton Mifflin Company. All rights reserved.