Convert Decimal to Fraction

To know about their conversion, firstly it is important to know what are decimals and what are fractions? Conversion of decimal to fraction and also vice-versa is the most used method in algebra, arithmetic or we can say whole parts of Mathematics.

Decimals-

The decimal word has been derived from the Latin word “Decima” which means “ a tenth part”.

Actually, Decimals are those numbers in which whole numbers and their fraction part are separated by a decimal point. Examples: 5.9, 54.67

Fractions

A fraction is denoting “a part of the whole”, it can be a number, area, etc.

Fraction number has two parts, i. Numerator and ii. Denominator

Actually, the Fraction is represented by ab .

Where  a = numerator and b = denominator

The following figure helps you in understanding fractions

Steps To Convert Decimals into fractions-

The following steps will help you in converting decimals into fractions, easily and accurately.

Step – 1: First and most basic step for this conversion is to write the given number in numerator and denominator form by taking 1 in the denominator.

Example, Convert 4.25 in fraction

ab =  4.251

Step – 2: Now, for conversion, you have to make the numerator a whole number by multiplying with multiples of 10. But it is necessary to keep in mind that you have to multiply in numerator and denominator.

ab =  4.25×10×1010×10 =  425100 

Step – 3: Simplify the obtained fraction, by dividing the numerator and denominator both with a common number.

ab  =  425100=  8520=  174

Finally, you will get the fraction that is converted from decimal.

Steps To Convert Repeating decimal to fractions

Along with simple decimal numbers, we also have some decimal numbers in which a digit after the decimal point is repeating itself to infinity. Now, it’s time to learn how you will convert these numbers into fractions.

Recurring Number = The decimal, in which digits after decimal point repeat themselves.

Step – 1: Example, Convert 0.888888…. to a fraction

Let, y = recurring number i.e., 0.88888…..

N = No of recurring digit = 8

Multiply the given recurring number by 10.

⇒  10y=8.888888

Step – 2: ⇒  10y-y=8

9y = 8

y = 8/9

Steps to Convert Decimals into Mixed Fractions

Well, Do you know what is Mixed Fractions?

Those Fractions on dividing which have a value greater than 1 are known as Mixed Fractions.

The following steps can help you in converting decimals to mixed fractions:-

Step – 1: Consider the two different parts of the decimal number separately.

Step – 2: Write the decimal part of a decimal number in a fraction using the steps we have discussed earlier. By removing the decimal point and dividing it by powers of 10 same as a number of digits after the decimal point.

Step – 3: Now, simplify the fraction that is obtained in step -2.

Step – 4: Attach the whole number part of the given decimal with the obtained fraction in step – 3, that is after simplifying.

For example, Convert 4.25 into a mixed fraction.

Step – 1: Whole Number Part = 4 , Decimal Part = 0.25

Step – 2:  Convert 0.25 into fraction,

ab= 0.251= 25100= 14

Step – 3: Attach with decimal Part,

Mixed Fraction = 414 .

Table Decimal To Fraction:-

Some commonly used fractions are given in the table.

Solved Examples-

 1: Find the fraction form of the decimal 0.6

    Given the decimal number 0.6, we need to convert it into the fraction for 0.6.

We can even find equivalent fractions by finding their multiples.

0.6 = 610

We can simplify  it, 

610= 35

Now multiply, 6/10 by 2, both in numerator and denominator, then we get;

(6×2)/(10×2) = 12/20

Also, we can find more equivalent fractions, by multiplying 6/10 by 5 and 10 both in the numerator and denominator.

6×5/10×5 = 30/50

6×10/10×10 = 60/10

Also, we can also multiply 35 in order to get more equivalent fractions.

Therefore, the fractions of 0.7 decimal are 7/10, 35/50, and 70/100.

2: Asha has started reading a new biography. Out of 300 pages, she read 30 pages in a day. What fraction of pages did she read in a day? Convert that fraction into decimals.

Solution:

Total number of pages = 300

Pages read by her in a day = 30

The fraction of pages read by her in a day = 30300 = 110

 ∴ That means, She read 1/10 or 0.1 pages in a day.

Conclusion-

You have read about how to convert decimals to fractions. To master this conversion, you should know division basics as well. We have discussed in detail all steps to convert decimals; into fractions. We have even discussed a step-by-step method for converting repeating decimals to fractions and also converting decimals into mixed fractions. By following that step-by-step procedure it is very easy to convert decimals into a fraction.