Decimal Fraction

What is a Decimal Fraction?

In algebra, a decimal fraction is a fraction whose denominator is 10 or a multiple of 10 like 100, 1000, 10000, etc. For example, 310 is a decimal fraction which is equivalent to 0.3.

Steps to Convert Decimal to Fraction

The steps given below shows how to convert decimal to fraction:

• Identify the place value of the last digit after the decimal in the number
• Use it to determine the denominator of the number
• Remove the decimal point and rewrite it in the fraction form
• Then reduce the fraction into its simplest form

Let us take an example to understand it better.

Example: Convert 0.25 into a fraction.

• Identify the place value of the last digit🡪 5 is in the hundredth place
• Therefore, the denominator of the number will be 100
• In fraction form 🡪25/100
• After simplifying it into the lowest equivalent fraction, we get 1/4

Steps to Convert Repeating Decimal into Fraction

Repeating decimals are those that do not terminate after a finite decimal place and a digit or digits keep on repeating itself. Let us take an example, 

Example: Convert 0.3333… to fraction.

Here the recurring digit is 3. 

Let x = 0.3333…

Multiplying 10 on both sides,

10x = 3.3333…

Subtracting both the equations,

9x = 3

x = 13.

Steps to convert decimal to mixed fraction number

Mixed fractions are those whose values are greater than 1. Decimal numbers whose values are greater than 1 can be written in the form of mixed fraction numbers. The steps are as follows:

• Take the whole number and the decimal part separately
• Check the place value of the last digit of the decimal number
• Use it to determine the denominator of the number
• Now write the whole number ignoring the decimal point in the form of a fraction
• Reduce it to the simplest form
• This will be the required form of the mixed fraction number

Example: Convert 4.5 into a fraction.

• Place value of the last digit 🡪 tenth place
• Denominator of the number is 10
• In fraction form 🡪 45/10
• Simplest form 🡪 9/2
• Mixed fraction for 🡪4 1/2

Steps to convert fraction to decimal

Case 1: If the denominator present in the number is 10 or multiple of 10.

Count the number of zeros in the denominator, then put the decimal point from the right by the same count. For example, if the fraction is 2100 then the number of zeros in the denominator is two. Then place the decimal point from two digits starting from the right. Hence, the answer will be 0.02.

Case 2: If the denominator is not a multiple of 10.

This can be treated as a simple division. For example, if 25 is to be converted from fraction to decimal. This can be simply seen as 2 ÷5. Hence, the answer comes out to be 0.4.

Conclusion 

Through this guide, we got to know about decimal numbers, fractions, decimal fractions, and their conversion to one another. Decimal numbers consist of whole numbers and fractional parts. Fraction number consists of a numerator and denominator. A decimal fraction is a fraction whose denominator is 10 or a multiple of 10.