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.

By definition, **a decimal fraction is a fraction that has its denominator as a power of ten**. For example, ** 3/10**,

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.

Convert the following fractions into decimal fractions.

a. *4**/**5*

b.*9**/**15*

c.*13**/**25*

d.*154**/**400*

b.

c.

d.

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*

b.

c.

d.

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.

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

a. *18**/**5*

b.*11**/**4*

c.*112**/**35*

b.

c.

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

Enjoy the "Decimal Fractions" math lesson? People who liked the "Converting Fractions to Decimals and Vice-versa lesson found the following resources useful:

- Decimal Fraction Feedback. Helps other - Leave a rating for this decimal fraction (see below)
- Fractions Math tutorial: Converting Fractions to Decimals and Vice-versa. Read the Converting Fractions to Decimals and Vice-versa math tutorial and build your math knowledge of Fractions
- Fractions Video tutorial: Converting Fractions to Decimals and Vice-versa. Watch or listen to the Converting Fractions to Decimals and Vice-versa video tutorial, a useful way to help you revise when travelling to and from school/college
- Fractions Revision Notes: Converting Fractions to Decimals and Vice-versa. Print the notes so you can revise the key points covered in the math tutorial for Converting Fractions to Decimals and Vice-versa
- Fractions Practice Questions: Converting Fractions to Decimals and Vice-versa. Test and improve your knowledge of Converting Fractions to Decimals and Vice-versa with example questins and answers
- Check your calculations for Fractions questions with our excellent Fractions calculators which contain full equations and calculations clearly displayed line by line. See the Fractions Calculators by iCalculator™ below.
- Continuing learning fractions - read our next math tutorial: The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions

We hope you found this Math tutorial "Converting Fractions to Decimals and Vice-versa" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.

- Operations With Fractions Calculator
- Recurrent Decimals To Fraction Converter
- Writing Fractions In The Lowest Terms Calculator
- Equivalent Fractions Calculator
- Equivalent Fractions Table Calculator
- Fraction Calculator
- Fraction To Ratio Calculator
- Ratio To Fraction Calculator
- Simplifying Complex Fractions Calculator
- Ordering Fractions Calculator
- Which Fraction Is Bigger
- Which Fraction Or Percentage Is Bigger
- Which Ratio Or Fraction Is Bigger