Decimal Fraction - Definition, Conversions, Examples

What is a Decimal Fraction?

A decimal fraction shows parts of a whole number using a dot called a decimal point. The digits after the decimal point represent smaller parts of one whole. For example, 0.5 means five-tenths, and 0.25 means twenty-five hundredths.

When you change a normal fraction into a decimal fraction, you replace the fraction line with a decimal point. For instance, 1/2 becomes 0.5, 3/10 becomes 0.3, and 7/100 becomes 0.07. 

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Numerator and Denominator of Fractions

A fraction shows how many parts of a whole are taken. It is written in the form a/b, where a and b are numbers. The number on the top is called the numerator, and the number on the bottom is called the denominator.

The numerator tells how many parts we have, and the denominator tells how many equal parts the whole has been divided into. For example, in 2/5, the numerator 2 means we have two parts, and the denominator 5 means the whole is divided into five equal parts.

Here are some important facts about fractions:

• If the numerator and denominator are the same, the value of the fraction is 1. For instance, 6/6 = 1.

• If the numerator is 0, the fraction’s value is also 0. For example, 0/9 = 0.

• If the denominator is 0, the fraction has no meaning because we cannot divide by zero.

Read More: Numerator and Denominator

Place Value of Decimal Fractions

We know that for whole numbers, the place value of digits starts from ones, tens, hundreds, thousands, and continues to the left. For example, in the number 452, the digit 2 is in the ones place, 5 is in the tens place, and 4 is in the hundreds place.

However, in the case of decimal fractions, the digits after the decimal point represent parts of one whole, and their place values move from left to right. Each place value represents a smaller part of the whole number.

Here is the order of place values after the decimal point:

• Tenths

• Hundredths

• Thousandths

• Ten-thousandths

For example:

• In 0.5, the 5 is in the tenths place.

• In 0.25, the 5 is in the hundredths place.

• In 0.347, the 7 is in the thousandths place.

• In 0.4562, the 2 is in the ten-thousandths place.

So, the place value of decimal fractions always decreases by ten times as we move right after the decimal point. Each position represents one-tenth of the previous one

Operations on Decimal Fractions

In mathematics, there are four main operations: addition, subtraction, multiplication, and division. These operations can also be done with decimal fractions.

Working with decimal fractions is simple when you follow the right steps. You just need to keep the decimal points in the correct place while adding or subtracting, and count the decimal digits properly when multiplying or dividing. Let’s look at how each operation works.

Addition of Decimal Fractions

When doing addition of decimal fractions, write the numbers one below the other and make sure the decimal points are in a straight line. Then, add each column just like normal numbers.

For example: 0.5 + 0.25 = 0.75

You can see that the addition of decimal fractions is simple if you remember to line up the decimal points correctly.

Subtraction of Decimal Fractions

To do subtraction of decimal fractions, also line up the decimal points before subtracting. Subtract each digit as you would with whole numbers.

For example: 0.9 − 0.4 = 0.5

So, when you practise subtraction of decimal fractions, always check that the decimal points are in the same column before starting.

Multiplying Decimal Fractions

When multiplying decimal fractions, you first multiply the numbers as if there were no decimal points. After that, count the total number of digits after the decimal points in both numbers. Then, place the decimal point in the answer.

For example: 0.3 × 0.2 = 0.06

This rule works for all multiplying decimal fractions and makes it easy to find the product.

Dividing Decimal Fractions

To perform division of  decimal fractions, first move the decimal point in the divisor (the number you are dividing by) so that it becomes a whole number. Then, move the decimal point in the dividend (the number being divided) the same number of places to the right. After that, divide as you would with whole numbers.

For example: 0.8 ÷ 0.2 = 4

Let’s look at another example: 1.5 ÷ 0.5 = 3

By shifting the decimal points equally, dividing decimal fractions becomes as easy as regular division.

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Types of Decimal Fraction

Decimals are classified into the following types based on the number of digits that come after the decimal point. Each type shows a different way decimal numbers can appear.

1. Terminating Decimal Fractions

A terminating decimal fraction ends after a certain number of digits. It does not continue forever.

Examples: 0.3, 0.75, 2.5 

These decimals stop after one or more places. For example, 3/10 = 0.3 and 3/4 = 0.75.

2. Non-Terminating Decimal Fractions

A non-terminating decimal fraction has digits that go on endlessly after the decimal point. It never stops.

Examples: 0.333…, 0.142857…

These numbers continue without ending because their fraction forms have denominators that do not divide evenly into powers of 10.

3. Recurring Decimal Fractions

A recurring decimal fraction repeats the same number or a group of numbers after the decimal point.

Examples: 0.666…, 0.121212…

4. Non-Recurring Decimal Fractions

A non-recurring decimal fraction has digits that do not repeat and do not follow any pattern.

Examples: 0.1010010001…, 1.414213…

These decimals continue forever but never repeat the same sequence of digits.

Read More: Like Fractions And Unlike Fractions 

Decimal Fractions Solved Examples

Example 1: Write 3/4 as a decimal fraction.

Solution: To convert a normal fraction into a decimal fraction, divide the numerator by the denominator.

3 ÷ 4 = 0.75

So, 3/4 = 0.75.

This means the fraction three-fourths is the same as seventy-five hundredths.

Example 2: Add 2.45 and 1.3.

Solution: When adding decimal fractions, write the numbers one below the other so that the decimal points are lined up.

 2.45  

+ 1.30   

………..

  3.75  

………

So, 2.45 + 1.3 = 3.75.

Always remember to line up the decimal points correctly while adding decimal fractions.

Example 3: Subtract 0.45 from 2.6.

Solution: Write both numbers so that the decimal points are in a straight line, then subtract as usual.

 2.60  

- 0.45  

……..

 2.15  

……..

Hence, 2.6 − 0.45 = 2.15.

When doing subtraction of decimal fractions, fill in any missing zeros to make subtraction easier.

Example 4: Multiply 0.4 by 0.2.

Solution: Ignore the decimal points and multiply the numbers as whole numbers:

4 × 2 = 8.

Now count the total number of digits after the decimal in both numbers. There are two digits (one in each).

So, place the decimal two places from the right: 0.08.

 Therefore, 0.4 × 0.2 = 0.08.

Example 5: Divide 0.9 by 0.3.

Solution: To perform dividing decimal fractions, move the decimal point in the divisor (0.3) one place to the right to make it a whole number (3). Move the decimal point in 0.9 the same way, which becomes 9.

Now divide 9 ÷ 3 = 3.

So, 0.9 ÷ 0.3 = 3.

Also Read: Unit Fraction

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