Decimal Fraction

To recall we know that a Fraction is formed up of two parts - Numerator and Denominator.

And expressed as -  Numerator/Denominator.

A Fraction or a Mixed Number in which the Denominator is a power of 10 such as 10, 100, 1000. etc. usually expressed by use of the Decimal point is termed as Decimal Fraction Math. Writing the Fraction in terms of Decimal makes it easier to carry on Mathematical Operations on them. For example any Fraction which has a Denominator as power of 10 like 53/100 can be written in Decimal as 0.53.

Examples of Decimal Fractions

4/100 = 0.04

57/10 = 5.7

53/100 = 0.53

The Right Way to Study about Decimals

Read the entire Number part first, followed by "and," and then read the Fractional component in the same way as Whole Numbers, but with the last digit's place value. Individual digits are always read as a Decimal Number. A Decimal Number of 145.367, for example, might be interpreted as one hundred forty-five point three six seven.

What is Decimal Fraction?

A Fraction where the Denominator i.e the bottom Number is a power of 10 such as 10, 100, 1000, etc is called a Decimal Fraction. You can write Decimal Fractions with a Decimal point and no Denominator, which make it easier to do calculations like addition, subtraction, division, and multiplication on Fractions.

Some of the Decimal Fractions examples are

1/10 th = read as one-tenth = written as 0.1 in Decimals.

6/1000 th = read as six-thousandths = written as 0.006 in Decimals

Operations on Decimal Fractions:

• Addition and Subtraction of Decimal Fractions:

The given Numbers are so placed under each other that the Decimal points lie in one column below one another. The Numbers are now added or subtracted in the regular way.

For example: add 0.007 and 3.002

0. 0 0 0 7

                     + 3. 0 0 0 2

          ____________________

          3. 0 0 0 9

• Multiplication of a Decimal Fraction: 

When a Decimal Fraction is multiplied by the powers of 10, shift the Decimal point to the right by as many places as is the power of 10.

For example, 5.9632 x 1000 = 5963.2;  

0.073 x 1000 = 730.

Multiply the given Numbers without a Decimal point. Now, in the product, the Decimal point is marked as many places of Decimal as is the sum of the Number of Decimal places in the given Numbers.

For example:  we have to find the product 0.2 x 0.02 x 0.0002

Consider the Number without Decimal points

Now, 2 x 2 x 2 = 8.

 Sum of Decimal places = (1 + 2 + 4) = 7.

Thus mark the Decimal point 7 places to the left that will be 0.0000008

 .2 x .02 x .002 = .0000008

• Dividing a Decimal Fraction By a Counting Number: 

Divide the given Number without the Decimal point, by the given Number. Now, in the quotient, mark the Decimal point as many places of Decimal as there are in the dividend.

For Example we have to find the quotient  for 0.0204 ÷ 17 

Now, 204 ÷ 17 = 12.

Dividend contains 4 places of Decimal. 

So, 0.0204 ÷ 17 = 0.0012

• Dividing a Decimal Fraction By a Decimal Fraction:

Multiply both the dividend and the divisor by a suitable power of 10 to make the divisor a whole Number.

Now, proceed as above.

How to convert Decimal to Fraction

You can convert a Decimal to a Fraction by following these three steps.

Let us convert 0.25 in Fraction

Step 1: Rewrite the Decimal Number over one as a Fraction where the Decimal Number is the Numerator and the Denominator is one.

0.25/1

Step 2: Multiply both the Numerator and the Denominator by 10 to the power of the Number of digits after the Decimal point. If there is one value after the Decimal point, multiply by 10, if there are two values after the Decimal point then multiply by 100, if there are three values after the Decimal point then multiply by 1,000, and so on.

For converting 0.25 to a Fraction, there are two digits after the Decimal point. Since 10 to the 2nd power is 100, we have to multiply both the Numerator and Denominator by 100 in step two.

0.25/1  x 100/100  = 25/100

Step 3: Express the Fraction in Decimal Fraction form and simplest form.

25/100  = ¼

By following these steps in the above Decimal Fraction questions, you can conclude that the Decimal 0.25, when converted to a Fraction, is equal to 1/4.

Let us solve Decimal questions.

Solved Examples

Decimal Fractions questions

Convert the given fractions into decimal fractions:

1. ½

Solution: ½ x 5/5  

= 5/10 

= 0.5

2. 10 ¼

Solution: 10 ¼

= 10 ¼ x 25/25

= 10 (25/100)

= 10.2

Quiz Time

1. Jim purchased 100 apples from a local fruit dealer, only to discover that five of them were rotting. Can you calculate the Fraction and Decimals of the rotten apples in relation to the total apples purchased by Jim?

Ans: Out of 100 apples, we have 5 rotten ones. As a result, the Percentage of rotten oranges is 5/100. Now we must convert this Fraction to a Decimal. We must divide the Numerator 5 by the Denominator 100 to achieve this. As a result, by adding two Decimal places to the Fraction 5/100, it can be converted to a Decimal. 0.05 is the Decimal answer. As a result, the rotten apples are 0.05 in Decimals.

2. In an 80-student class, 48 pupils chose ice cream as a snack, while the other students preferred soft drinks. Calculate the Percentage of students that choose a soft drink and give the result in Decimals.

Ans: There are 80 pupils in a class, 48 students who enjoy ice cream, and 80 - 48 = 32 students who enjoy soft drinks. Soft drinks are enjoyed by 32 percent of students out of 80. This Fraction is equivalent to 2/5 on simplification. Let's convert this Fraction to a Decimal and then to a Percentage. To convert the Fraction to a Decimal, divide 2 by 5, and the result is 0.4. In order to convert 0.4 to a Percentage, we must multiply it by 100, which is 0.4 x 100 percent = 40%. As a result, the Percentage of students who enjoy soft drinks is 40%, and the Decimal equivalent is 0.4.

3. Write 1/4th in Decimals.

Ans: Let's look at how to express 1/4 in Decimals. To get a 100 in the Denominator, multiply the Numerator and Denominator with a 25. We also need to convert this Fraction to a Decimal with a Denominator of 100.

0.25 = 1/4 x 25/25 = 25/100