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# Convert Decimals to Fractions – Explanation & Examples

Before we learn how to convert decimals to fractions, there are a number of basic information we need to know about decimals and fractions. To start with, a decimal number is probably a number which has a dot (.) between the digits, this dot is known as a decimal point. Basically, decimal numbers are just fractions having a denominator expressed in power of 10. Example of decimal numbers are: 0.005, 3.2, 10.9, 55.1, 1.28, 9.234, etc.

A fraction on the other hand is portion of a whole number usually denoted as a ratio of two integers a/b. The two integers a and b are referred to as the numerator and denominator respectively. There are three types of fractions namely: Proper, Improper and Mixed fraction. Examples of fractions are, 5/8, 7/3 and 2 ^{1}/_{5.}

## How to Convert Decimal to Fraction?

We can easily convert a decimal number into a fraction by following simple steps and no calculators are required. This article has elaborated clearly all the steps of converting decimals to fractions, with some examples.

*Let us learn these steps on to convert the decimal into fractions:*

- First, begin by counting the numbers to the right side after the decimal point.
- Let n be the number of digits on the right side after the decimal point.
- Write the number without a decimal point as a numerator and the power of 10
^{n}as the denominator - Now the fraction can be simplified by reducing the denominator and numerator with a common factor.
- The simplified fraction is the required fraction from the given decimal number.

Let us solve the following examples so get a better understand of how to convert a decimal into fraction.

*Example 1*Convert 0.7 to a fraction.

__Solution__

- The number 0.7 has only one decimal place, therefore our n is 1.
- Take the number as a numerator by ignoring the decimal point. Take also the power of 10
^{1}as the denominator. - Now our fraction is 7/ 10
^{1}. And since 10^{1}= 10, then our fraction is 7/10. - The fraction is already in its lowest terms, therefore, 7/10 is our answer.

*Example 2*

Convert 0.05 to a fraction and simplified it in the lowest form.

__Solution__

- The number 0.05 contain two decimal places, therefore n = 2.
- Ignore the decimal point and write the number as the numerator and take also 10
^{2}to be the denominator - Since 10
^{2 }is the same as 10 x 10 = 100, the write the number in fractional form: 5/100. - Because the both the numerator and denominator have a common factor, then the fraction can be simplified to the lowest terms: 5/100 = 1/20
- Therefore, the answer is 1/20

*Example 3*

Convert the decimal number 5.066 into a fraction.

__Solution__

- First count the number of decimal places. The number of decimal places in 5. 066 is 3. Therefore, n = 3
- Write the decimal as a whole number and divide it by 10
^{3}. You can notice that dividing the number is the same as writing it in fractional form. - Since 10
^{ 3 }= 10 x10 x 10 = 1000, Now the number in fractional form is 5066/1000. - By just looking at the last digits both the numerator and denominator, the numbers are even.
- Simplify the fraction: 5066/1000 = 2533/500
- The fractional can not be simplified further, and hence the answer is 2533/500

*Example 4*

Convert 0.0035 into fraction

__Solution__

- In this case, the number of decimal places in the number is 4. Therefore, n = 4.
- Write the number without a decimal point and divide by 10
^{4}=10 x 10 x 10 x 10 = 10000 - 0035 = 35/10000. Both the denominator and numerator have common factors, therefore simplify the fraction to its lowest form.
- 35/10000 = 7/2000.
- Thus, the answer is 7/2000.

### How to Convert a Repeating Decimal to Fraction?

Repeating or recurring numbers are decimal numbers with the endless repeating decimal digits. Either there can be a single digit repeating or two and more digits repeating by alternating. Examples of repeating numbers are: 0.3333333…., 0.666…, 4.2525252525…, 0. 56111., etc.

To convert a repeating number into a fraction, see the following example.

*Example 5*

** **Convert the repeating number 0.6666… Into fraction.

__Solution__

Let r be the repeating number: r = 0.6666

Multiply both sides of the multiplication sentence by 10.

10 x = 6.666…

Perform the subtract on both sides of the equation as shown below;

(10x – x) = (6.6666 – 0 .666)

9x = 6.000

Now divide both sides by 9;

x = 6/9

Simplify the fraction to its lowest terms

x = 6/9 = 2/3

Hence, 0.6666…= 2/3

Therefore 2/3 is fraction from a recurring number 0.6666666…..