 # Decimal Fraction

## Decimal Fraction Math

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

### 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:

1. 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.

1. 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.

 Thus, 0.00066 = 0.00066 x 100 = 0.066 = .006 0.11 0.11 x 100 11

### 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  = 1/4

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 fraction into decimal fraction

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)

= 10.25

### Quiz Time

Decimal fraction questions

Convert the fractions into decimal fractions

1. 64 ⅜

2. 5/4

3. 72(5/2)

4. 1/100

1. How to Simplify Fractions

There are basically  two methods to simplify fractions into its simplest form.

Method 1

Try to divide both the numerator and denominator of the fraction by 2, 3, 5, 7, …...etc, until we cannot go any further.

For example, simplify the fraction 28 / 128.

Solution:

28/ 70 ÷ 2 = 14 /35

14 / 35  ÷ 7 = 2 /  5

Now you cannot further divide this fraction with the common number.

Thus, the fraction  2 / 5 is in the simplest form.

Method 2

Multiplying by a single will be a lengthy process in case of large numbers. A better and shorter way to simplify fractions is to find out  the highest common factor (HCF) of the numerator and denominator and divide both of them by it.

For example: Simplify fraction to its simplest form 8 / 20.

Solution: The highest common factor of numerator and denominator i.e of 8 and 20 is 4.

Now, divide both the numerator and denominator by 4 and you get

8 / 20 ÷ 4 = 2 / 5

So, the simplest form is 2 / 5.

2. What is Recurring Decimal?

If in a decimal fraction, a number or a set of numbers keeps on repeating continuously, then such a number is called a recurring decimal.

in a recurring decimal, if a single number is repeated, then it is expressed by putting a dot on it. If a set of numbers are repeated, it is expressed by putting a bar on the set.

Thus, 1/3  = 0.333…

= 0.3

22/7 =  3.142857142857…..

= 3.148257

A decimal fraction, in which all the numbers after the decimal point are repeated, is called a pure recurring decimal.