# Math Lesson 3.5.3 - Converting Decimals to Fractions

[ No Votes ]

Welcome to our Math lesson on Converting Decimals to Fractions, this is the third 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.

## Converting Decimals to Fractions

The key point in this process is to know how to write the decimal as a mixed number. The rest is already a known procedure. Let's consider an example in this regard.

### Example 5

Convert the following decimals into improper fractions.

a. 8.4
b. 5.03
c. 123.7
d. 76.008

### Solution 5

1. From theory, we know that the whole part of 8.4 is 8 and its decimal part is 4. In addition, the denominator of the corresponding mixed number is 10 because 8.4 has one decimal place. Hence, we have
8.4 = 8 4/10
When written as an improper fraction, this number becomes
8 4/10 = (8 × 10 + 4)/10 = 84/10
2. From theory, we know that the whole part of 5.03 is 5 and its decimal part is 04. In addition, the denominator of the corresponding mixed number is 100 because 8.04 has two decimal places. Hence, we have
5.03 = 5 3/100
When written as an improper fraction, this number becomes
5 3/100 = (5 × 100 + 3)/100 = 503/100
3. From theory, we know that the whole part of 123.7 is 123 and its decimal part is 7. In addition, the denominator of the corresponding mixed number is 10 because 123.7 has one decimal place. Hence, we have
123.7 = 123 7/10
When written as an improper fraction, this number becomes
123 7/10 = (123 × 10 + 7)/10 = 1237/10
4. From theory, we know that the whole part of 76.008 is 76 and its decimal part is 008. In addition, the denominator of the corresponding mixed number is 1000 because 76.008 has three decimal places. Hence, we have
76.008 = 76 8/1000
When written as an improper fraction, this number becomes
76 8/1000 = (76 × 1000 + 8)/1000 = 76008/1000

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

Fractions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
3.5Converting Fractions to Decimals and Vice-versa
Lesson IDMath Lesson TitleLessonVideo
Lesson
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

## Whats next?

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

1. Decimal To Fraction Feedback. Helps other - Leave a rating for this decimal to fraction (see below)
2. 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
3. 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
4. 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
5. 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
6. 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.
7. Continuing learning fractions - read our next math tutorial: The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions

## Help others Learning Math just like you

[ No Votes ]

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.