 # Decimals, Fractions, and Percents

I. Decimals
A. Converting Decimals into Fractions
1. Put the entire number into the numerator of the fraction with the
decimal removed .
2. Count the number of digits after the decimal point and place a 1 followed
by that many zeros in the denominator in the fraction .
3. Reduce the fraction if possible (see our Fractions handout for additional
help in reducing fractions ).
a) Example 1: Convert 8.453 into a fraction. b) Example 2: Convert 0.04 into a fraction. B. Converting Decimals into Percents
1. Move the decimal point two places to the right.
a) Example 3: Convert 1.3 into a percent. b) Example 4: Convert 0.04 into a percent. II. Fractions
A. Converting Fractions into Decimals
1. Divide the numerator of the fraction by the denominator.
2. If you get a remainder, write a zero next to the remainder and continue
dividing. Remember to include the decimal place both under the division
3. Continue dividing until you get a repeating decimal or until the division
ends (you have no remainder).
a) Example 5: Convert 8/5 into a decimal. b) Example 6: Convert 9/2 into a decimal. B. Converting Fractions into Percents
1. There are two ways to do this.
1. One way is to first convert the fraction into a decimal, and then
convert that decimal into a percent.
(1) Example 7: Convert 3/2 into a percent. 2. The other way is to set up a proportion with the fraction set equal to
x over 100. To solve a proportion , you cross multiply and set the two
results equal to each other. Then solve the equation .

(1) Example 8: Convert 3/2 into a percent III. Percents
A. Converting Percents into Decimals

1. Move the decimal point two places to the left.

a) Example 9: Convert 48.3% into a decimal b) Example 10: Convert 7% into a decimal B. Converting Percents into Fractions
1. There are two ways to convert a percent into a fraction.
a) One way is to first convert the percent into a decimal. Then
convert that decimal into a fraction. Once you have your fraction,
reduce the fraction if possible (if you need help reducing
fractions, see our Fractions handout).
(1) Example 11: Convert 15% into a fraction b) Another way is to put the percent over 100. If there is a decimal
in the percent, add an extra zero to 100 for each number after the
decimal point. Then reduce.

(1) Example 11: Convert 34% into a fraction. (2) Example 12: Convert 2.35% into a fraction. Sample Problems
Convert each decimal into a fraction.

1. 0.57
2. 0.06
3. 1.2
4. 0.036
5. 15.75
6. 8.16

Convert each decimal into a percent.

7. 0.67
8. 1.009
9. 0.000007
10. 0.952
11. 0.04
12. 1

Convert each fraction into a decimal. Convert each fraction into a percent. Convert each percent into a decimal.

25. 51%
26. 31.2%
27. 6%
28. 410%
29. 0.17% Convert each percent into a fraction.

31. 31%
32. 65%
33. 0.5%
34. 220%
35. 7.75%
36. 100%

Convert each decimal into a fraction. Convert each decimal into a percent.

7. 67%
8. 100.9%
9. 0.0007%
10. 95.2%
11. 4%
12. 100%

Convert each fraction into a decimal. Convert each fraction into a percent.

19. 87.5%
20. 750%
21. 12.5%
22. 43.75%
23. 7.8125% Convert each percent into a decimal.

25. 0.51
26. 0.312
27. 0.06
28. 4.10
29. 0.0017 Convert each percent into a fraction. Prev Next