Math Lesson 3.5.1 - Decimal Fractions

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Welcome to our Math lesson on Decimal Fractions, this is the first lesson of our suite of math lessons covering the topic of Converting Fractions to Decimals and Vice-versa, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Decimal Fractions

By definition, a decimal fraction is a fraction that has its denominator as a power of ten. For example, 3/10, 21/100, 357/1000, etc., are all decimal fractions because we can write them as

3/10 = 3/101
21/100 = 21/102
357/1000 = 357/103

There are some fractions that do not seem to be decimal fractions, but with a few steps, they can be transformed into decimal fractions. These steps include multiplying or dividing both numerator and denominator several times by the same number until we obtain a decimal fraction. First, we check whether the denominator may become 10 or not; otherwise we try for 100, then for 1000 and so on. Let's see an example to clarify this point.

Example 1

Convert the following fractions into decimal fractions.

a. 4/5
b. 9/15
c. 13/25
d. 154/400

Solution 1

We have

a. 4/5 = (4 × 2)/(5 × 2) = 8/10
b. 9/15 = (9 ÷ 3)/(15 ÷ 3) = 3/5 = (3 × 2)/(5 × 2) = 6/10
c. 13/25 = (13 × 4)/(25 × 4) = 52/100
d. 154/400 = (154 ÷ 2)/(400 ÷ 2) = 77/200 = (77 × 5)/(200 × 5) = 385/1000

Despite the fact that in the example above we have considered only proper fractions, decimal fractions can also be improper. In this case, it is better to write them as mixed numbers. Let's see another example to clarify this point.

Example 2

Express the following fractions into mixed numbers after converting them into decimal fractions first.

a. 18/5
b. 11/4
c. 112/35

Solution 2

  1. We have
    18/5 = 36/10 = 36 ÷ 10 = 3 (6) = 3 6/10
  2. Also,
    11/4 = (11 × 25)/(4 × 25) = 275/100 = 275 ÷ 100 = 2 (75) = 2 75/100
  3. Likewise,
    112/35 = (112 ÷ 7)/(35 ÷ 7) = 16/5 = (16 × 2)/(5 × 2) = 32/10 = 32 ÷ 10 = 3 (2) = 3 2/10

Not all fractions can be written as decimal fractions. For example, the fraction 2/3 cannot be expressed as decimal fraction because it is impossible to find a whole number that when multiplied by 3 gives a power of 10. We will discuss later for such fractions on how to deal with them.

More Converting Fractions to Decimals and Vice-versa Lessons and Learning Resources

Fractions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
3.5Converting Fractions to Decimals and Vice-versa
Lesson IDMath Lesson TitleLessonVideo
3.5.1Decimal Fractions
3.5.2The Meaning of Decimals. Converting Fractions into Decimals without a Calculator
3.5.3Converting Decimals to Fractions
3.5.4Converting Recurrent Fractions into Decimals

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  7. Continuing learning fractions - read our next math tutorial: The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions

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