Fractions to Decimals

Fractions such as 9/10, 37/100, or 111/1000, with a denominator of a power of ten are the easiest to convert to a decimal. Why? Let’s recall the place value positions of decimals.
0.1234 --- > the “1” is in the one tenths place; the “2” is in the one hundredths place; the “3” is in the one thousandths place, and the “4” is the ten-thousandths place.

Read the fraction aloud, and you have the decimal name. Read 9/10 as nine tenths. Then write 0.9 with the nine in the tenths place. Here are a few examples.

a) 37/ 100 = 0.37

b) 3/100 = 0.03 note: Read as three one-hundredths; therefore, the 3 needs to end up in the hundredths place, and place a zero in the tenths place.

c) 111/1000 = 0.111

d) 4/1000 = 0.004

What if the fraction is 2/5? In other words, the denominator is not a power of ten.

Well, the fraction bar tells you what to do. The fraction bar indicates division. So, you can read 2/5 as two “divided by” 5. Do the math and the result is “0.40.” Try ¼ means one divided by four, and the answer is “0.25.”

Convert 3/8 into a decimal. Remember to write as you say, “three divided eight.” Hint, this fraction has three decimal places. Sometimes, your result may end up as a repeating decimal. Then, it’s okay to stop after the repeat pattern and put a “-“over the digit to indicate it repeats. By the way, the answer for converting 3/8 to a decimal is 0.375.

In order to convert a mixed number to a decimal, the whole number is unchanged. Convert the fraction and write it behind the whole number. For example: 3 4/5 = 3.80. the “3” in the decimal number comes from the whole number in the fraction. The “.80” is the result of 4 being divided by 5. Likewise, 7 ½ = 7.50.

Practice I:
Write the following fractions as decimals.
1) 6/10 =
2) ¾ =
3) 56/1000 =
4) 5/8 =
5) 7/8 =
6) 9/100 =
7) 2 ¼ =
8) 5 3/5
9) 2 ½ =
10) 35/100

Converting Decimals to Fractions
Once again, read the decimal properly, and you have your answer. Many people read “0.3” as “point three.” I call this the nick name and, it’s not correct. The three is in the tenths place. Therefore, read “0.3” as three tenths, and you have your answer. 0.3 = 3/10.

0.65 is read as sixty-five hundredths; thus the fraction is 65/100. Remember to reduce the fraction. Then, the final answer is 13/20.

Practice II
Convert the following decimals to fractions.
1) 0.8 =
2) 0.505 =
3) 0.35 =

Let’s look at the decimal, “2.5.” Read as two and five tenths. Notice, “2” is the whole number, and the word “and” is said for the decimal. Thus, the fraction for 2.5 is 2 5/10. Remember to reduce, and the final answer is 2 ½.

Another example: 4.005 = 4 5/1000 = 4 1/200

Practice III:
Convert to fractions.
1) 6.3
2) 9.2
3) 4.35
4) 7.025

Answers for Practice I:
1) .6
2) .75
3) .56
4) .625
5) .875
6) .09
7) 2.25
8) 5.60
9) 2.50
10) .35

Answers for Practice II:
1) 8/10 = 4/5
2) 505/1000 = 101/200
3) 35/100 = 7/20

Answers for Practice III:
1) 6 3/10
2) 9 2/10 = 9 1/5
3) 4 35/100 = 4 7/20
4) 7 25/1000 = 7 1/40


More practice ideas: