One of the most common arithmetic operations is changing decimals to fractions and fractions to decimals. However, to do so, we must first understand the basics of division. Decimals can be converted to fractions by densifying the digits’ place value in the number after the decimal. Use this to figure out what the fraction’s denominator will be. Remove the decimal point from the equation. Simplify it by rewriting it in fraction form. 

In this article, let us learn how to change decimal to fraction and vice versa. 

What are Fractions?

A fraction is a number that represents a whole number that has been divided evenly into equal parts. The numbers of the form \(\frac{a}{b}\) where \(a\) and \(b\) are natural numbers, which are called fractions.

Here, \(a \to \) numerator and \(b \to \) denominator.
Examples: \(\frac{3}{6} ,\frac{{15}}{{30}},\frac{1}{5},\frac{3}{{19}} \ldots \)

Decimals

A decimal point is a dot placed between two integers in a group of numbers called a decimal. Integers or whole numbers are numbers to the left of the decimal point, and decimal numbers are numbers to the right of the decimal point. The first digit after the decimal point will be the one-tenth position. 

Examples: \(34.8.\) Here, the digit \(8\) is in the one-tenth position

The second digit after the decimal point will be one-hundredth position. 

Examples: \(124.86.\) Here, digit \(6\) is in the one-hundredth position.

Decimal Fractions

A decimal fraction is one in which the denominator, or bottom number, is a power of ten, such as \(10, 100, 1000,\) and so on. We can write decimal fractions with a decimal point and no denominator, making it easier to give results on fractions such as addition, subtraction, division, and multiplication.

Examples:

\(\frac{1}{{10}} = 0.1\)

\(\frac{6}{{1000}} = 0.006\)

Changing Fraction to Decimal

Steps to convert a fraction to decimal are given below,

1. There are two parts to a fraction: a numerator and a denominator. It’s used to indicate how many parts we have compared to the total number.
Example: \(\frac{2}{4}\)
Here, \(2→\)numerator, \(4→\)denominator

2. The division symbol can be represented by a line that separates the numerator and denominator in a fraction.

3. Divide the numerator by the denominator to convert a fraction to a decimal. As a result, we will have a decimal answer.
Example: \(\frac{2}{4} = 0.5\)

Conversion of Mixed Fraction to Decimal

There are two methods for converting a mixed fraction to a decimal:

1. Divide the improper fraction after converting the mixed fraction to an improper fraction. 

Example: \(5\frac{1}{4} = \frac{{21}}{4} = 5.25\)

2. Convert the fractional part only, then add it to the whole number. In other words, convert the fraction while keeping the whole number the same.

Example: Change \(5\frac{3}{4}\) to decimal form.

We can write \(5\frac{3}{4}\) as \(5 + \frac{3}{4}\)

First, convert \(\frac{3}{4}\) into decimal form.

\( \Rightarrow \frac{3}{4} = \frac{{3 \times 25}}{{4 \times 25}} = \frac{{75}}{{100}} = 0.75\)

Now, \(5 + \frac{3}{4} = 5 + 0.75\)

\(=5.75\)

Conversion of Fractions to Decimals If the Denominators are 10,100, 1000…

When converting the fractions with denominators having \(10, 100, 1000,\) and so on into decimal numbers, the following steps are used:

Step 1: If the fraction does not have \(10, 100, 1000\) etc., convert it to an equivalent fraction with a denominator of \(10\) or \(100\) or \(1000.\)

Step 2: Find the numerator of the given fraction. If the denominator of the given fraction is \(10\) or \(100\) or \(1000,\) place the decimal point after one place, two places, or three places from right to left.

Note: If the numerator has fewer digits, add zeroes to the left of the numerator.

Example:  \(\frac{5}{{10}} = 0.5\)

Examples for Conversion of Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

Example-1: Convert \(\frac{3}{{10}}\) into decimal form.

Divide the numerator by the denominator.So, \(\frac{3}{{10}} = 0.3\)

Example-2: Convert  \(\frac{{40}}{{50}}\) to decimal form.

Multiply both the numerator and the denominator by \(2.\)

So, we have, \(\frac{{40}}{{50}} = \frac{{40 \times 2}}{{50 \times 2}} = \frac{{80}}{{100}}\)

\( \Rightarrow \frac{{40}}{{50}} = 0.8\)

Example-3: Convert \(\frac{20}{{100}}\) to decimal form.

Divide the numerator by the denominator.

So, \(\frac{{20}}{{100}} = 0.2\)

Example-4: Change \(8\frac{3}{4}\) to decimal form.

We can write \(8\frac{3}{4}\) as \(8 + \frac{3}{4}\)

First, convert \(\frac{3}{{4}}\) into decimal form.

So, \(\frac{2}{4} = \frac{{3 \times 25}}{{4 \times 25}} = \frac{{75}}{{100}} = 0.75\)

Now, \(8 + \frac{3}{4} = 8 + 0.75\)

\(8.75\)

Changing of Decimal to Fraction

Steps to convert a decimal to a fraction:

In this case, we shall use the decimal \(0.75\) as an example.

1. Rewrite the decimal number as a fraction using one as the denominator and the decimal number as the numerator.
2. Both the numerator and denominator should be multiplied by \(10\) to the power of the number of digits after the decimal point. If there is just one number after the decimal, multiply by ten; if there are two, multiply by one hundred; if there are three, multiply by one thousand, and so on.
3. Then, write the fraction in the simplest form. 
4. In the decimal number \(0.75,\) there are two digits after the decimal point. Hence, we must multiply the numerator and denominator by \(100\) because \(10\) to the \({{\rm{2}}^{{\rm{nd}}}}\) power is \(100.\)
   As a result, we have \(0.75 = \frac{{75}}{{100}} = \frac{3}{4}\)

Examples for Conversion of Decimals to Fractions

For the numerator of the fraction, write the given decimal number without the decimal point. For the denominator, write \(1\) followed by as many zeros as decimal places in the given decimal number.

Example-1: Convert \(0.8\) to fractional form.

In \(0.8\) there is only one decimal place.

So, \(0.8 = \frac{{8}}{{10}} = \frac{4}{5}\)

Example-2: Convert \(0.125\) to fractional form.

In \(0.125\) there are three decimal places.

So, \(0.125 = \frac{{125}}{{1000}} = \frac{1}{8}\)

Example-3: Convert \(0.0238\) to fractional form.

In \(0.0238\) there are four decimal places.

So, \(0.0238 = \frac{{0.0238}}{{10000}} = \frac{{119}}{{5000}}\)

Solved Examples

Q.1. Convert \(0.00098\) to a fraction.
Ans: Given decimal fraction is \(0.00098\)
To convert \(0.00098\) into a fractional number, first, we need to write in the numerator \(98,\) leaving out the decimal point and then write \(100000\) in the denominator since there are five digits after the decimal point.
Therefore, \(0.00098 = \frac{{98}}{{100000}} = \frac{{49}}{{50000}}\)

Q.2. Convert \(\frac{9}{{10}}\) to decimal.
Ans: To convert \(\frac{9}{{10}}\) to a decimal, divide the numerator by the denominator.
So, \(\frac{9}{{10}} = 0.9\)
Hence, the decimal form of \(\frac{9}{{10}}\) can be written as \(0.9.\)

Q.3. Express \(\frac{{356}}{{100}}\) in decimal form.
Ans: Given: \(\frac{{356}}{{100}}\)
We know if the denominator of the given fraction is \(10\) or \(100\) or \(1000,\) place the decimal point after one place, two places, or three places from right to left.
So, \(\frac{{356}}{{100}} = 3.56\)
Therefore, the decimal form of \(\frac{{356}}{{100}}\) can be written as \(3.56.\)

Q.4. Convert \(0.00178\) to a fraction.
Ans: Given decimal fraction is \(0.00178.\)
To convert \(0.00178\) into a fractional number, first, we need to write in the numerator \(178,\) leaving out the decimal point and then write \(100000\) in the denominator since there are five digits after the decimal point.
Therefore, \(0.00178 = \frac{{178}}{{100000}} = \frac{{89}}{{50000}}.\)

Q.5. Express \(\frac{{56}}{{10000}}\) in decimal form.
Ans: Given: \(\frac{{56}}{{10000}}\)
We know if the denominator of the given fraction is \(10, 100, 1000\) or \(10000,\) place the decimal point after one place, two places, or three, four places left of the rightmost digit of the number.
If the numerator has fewer digits, add zeroes to the left of the numerator.
So, \(\frac{{56}}{{10000}} = 0.0056\)
Therefore, the decimal form of  \(\frac{{56}}{{10000}}\) can be written as \(0.0056.\)

Q.6. Express \(\frac{7}{{1000}}\) in decimal form.
Ans: Given: \(\frac{7}{{1000}}\)
We know that if the denominator of the given fraction is \(10\) or \(100\) or \(1000,10000,\) place the decimal point after one place, two places, or three, four places left of the rightmost digit of the number.
If the numerator has fewer digits, add zeroes to the left of the numerator.
So, \(\frac{7}{{1000}} = 0.007\)
Therefore, the decimal form of \(\frac{7}{{1000}}\) can be written as \(0.007.\)

Q.7. Change \(7\frac{1}{4}\) to decimal form.
Ans: We can write \(7\frac{1}{4}\) as \(7 + \frac{1}{4}\)
First, convert \(\frac{1}{4}\) into decimal form.
So, \(\frac{1}{4} = \frac{{1 \times 25}}{{4 \times 25}} = \frac{{25}}{{100}} = 0.25\)
Hence, \(7 + \frac{1}{4} = 7 + 0.25 = 7.25\)
Therefore, \(7.25\) is the decimal form \(7\frac{1}{4}\)

Summary

Decimals can be written in fraction form. And also, the fractions can be converted into decimal numbers. This article includes the definitions of fractions, decimals, the procedure to be followed for changing decimals to fractions and fractions to decimals with examples.

This article, “changing decimal to fraction, fraction to decimal,” help in understanding these in detail, and it helps to solve the problems based on these very easily.

FAQs

Q.1. How do I convert a fraction to a decimal?
Ans: Divide the numerator by the denominator to convert a fraction to a decimal. We can do this with a calculator if required. As a result, we will have a decimal answer.
Example: \(\frac{1}{4} = 0.25\)

Q.2. How do you change 5.6 into a fraction?
Ans: As the numerator of the fraction, write the provided decimal without the decimal point. Write \(1\) followed by as many zeros as decimal places in the provided decimal in the denominator.
\( \Rightarrow 5.6 = \frac{{56}}{{10}} = \frac{{28}}{5} = 5\frac{3}{5}\)

Q.3. What is 0.3 converted to a fraction?
Ans: We know \(0.3 = \frac{3}{{10}}.\)

Q.4. What is 3/4 as a decimal?
Ans: \(0.75\) is \(\frac{3}{4}\) as a decimal

Q.5. How to convert decimal to fraction?
Ans: Steps to convert decimal to fraction are,
1. The numerator will be the decimal number without the decimal point
2. The denominator will have the number followed by as many zeros as the number of digits in the given decimal number
3. Reduce the fraction to its simplest form

Q.6. How do you convert mixed fractional numbers to decimals?
Ans: There are two methods for converting a mixed fraction to a decimal:
1. Divide the improper fraction after converting the mixed fraction to an improper fraction.
Example: \(7\frac{1}{4} = \frac{{29}}{4} = 7.25\)
2. Convert the fractional part to decimal only, then add it to the whole number. In other words, convert the fraction while keeping the whole number the same.

Now you are provided with all the necessary information on changing decimal to fraction, fraction to decimal and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.