Decimal fractions Math is the representation of the decimal form of fractions, whose denominator is 10 or higher powers of 10, like 100, 1000, 10000, etc. For example 1/10, 1/100, 1/1000, are fractions in decimal. If we simplify such fractions, we can write them in the decimal form such as 0.1, 0.01, 0.001, etc. It is easy to solve mathematical problems that are represented in the form of decimal fractions, such as dividing fractions, multiplying fractions, etc.

A fraction represents a part of the whole. For example, it tells how many slices of a pizza left or eaten with respect to the whole pizza-like, one-half, three-quarters. Generally, a fraction has two parts i.e. the numerator and the denominator. A decimal fraction is a fraction where its denominator is a power of 10 i.e. 10¹,10², 10³ etc.

What are Decimal Fractions?

The fractions in which the denominator is equal to 10 or multiples of 10 (such as 100, 1000, 1000, 10000, etc.), are known as decimal fractions.

Examples:

• 1/10 = 0.1
• 2/100 = 0.02
• 7/1000 = 0.007

Numerator and Denominator of Fractions

As we already know, fractions are the parts of something whole. It is represented as a/b, where a and b are the integers. The integer above the bar is the numerator and below the bar is the denominator.

The numerator states the number that is equal parts and denominator states the number of parts of a given number. Let us see here some of the conditions for fractions:

• If numerator and denominator have equal values then the fraction is 1.
• If numerator is equal to 0, then the fraction is 0.
• If denominator is equal to 0, then the fraction goes to infinity.
• A decimal fraction is known as a recurring decimal when the digit after the decimal keeps on repeating.

Place Value of Decimal Fractions

We know for the whole number, the place value of digits starts from ones, tens, hundreds, thousands, ten-thousands and so on, moving from right to left.

In the case of decimal fractions, since we are considering here the decimal point, thus the place value of digits are taken into account from left to right in the order of:

• Tenths
• Hundredths
• Thousandths
• Ten-thousandths

For example,  the place value of 5 in 0.25 is hundredths.  Follow the below table to learn the place value of digits in a number.

Operations on Decimal Fractions

As we know, there are four basic operations in Maths viz. addition, subtraction, multiplication and division.

It is easy to perform arithmetic operations on decimal fractions. Let us discuss the different operations performed on decimal fractions.

Addition of Decimal fractions

Suppose we need to add 2/100 and 3/10000. Then first we can simplify and write in decimal fraction form.

2/100 = 0.02

3/10000 = 0.0003

Now, adding the two values we have:

0.02 + 0.0003 = 0.0203

Thus, we can see, it is easy to add the fractions after writing them in decimal form.

Subtraction of Decimal fractions

The method of subtraction of decimal fractions is the same as addition. Let us understand by an example.

Subtract 0.008 and 0.002.

0.008 – 0.002 = 0.006 (By subtracting the digits at the thousandths place)

Multiplication of Decimal Fractions

When we multiply a decimal fraction by multiples of 10, then we have to shift the decimal point to the right as many places as the power of 10.

Example: Multiply 0.089 x 100

0.089 x 100 = 8.9

Division of Decimal Fractions

When we divide a decimal fraction by a whole number, then remove the decimal and divide it. Now, place the decimal point as many places as of the dividend.

Example: 0.081 ÷ 3

Remove the decimal point from 0.081 and then divide by 3.

81/3 = 27

Now place the decimal point up to three places of decimal.

0.081/3 = 0.027

It is the required answer.

Types of Decimal Fractions

The decimal fractions as discussed are the fractions whose denominators are in the multiples of 10. We have learned the types of decimals in Mathematics, such as:

• Terminating Decimals – has a finite number of digits after the decimal
• Non-Terminating Decimals – has infinite or non-terminating digits after the decimal
• Recurring Decimals – has repeating digits after the decimal
• Non-Recurring Decimals – has non-repeating digits after the decimal

Based on these categories we can say, the decimal fractions are more likely to be terminating and non-repeating.  Since, the denominator here is in the power of 10 and hence, will result in terminating decimal.

Solved Examples on Decimal Fractions

Example 1: A barrel has 56.32 litres capacity. If Supriya used 21.19 litres how much water is left in the barrel.

Solution: Given,

Capacity of the barrel = 56.32 liters

Amount of water used= 21.19 liters

Amount of water left in the barrel = 56.32 – 21.19 = 35.13 liters

Example 2: Megha bought 12 bags of wheat flour each weighing 4563/100  kg. What will be the total weight?

Solution:  Total no. of bags = 12

Weight of each bag =  4563/100 kg = 45.63 kg

Total weight =45.63 x 12=547.56 kg

Example 3: If circumference of a circle is 16.09 cm. What will be its diameter(π=3.14)?

Solution: Given, circumference = 16.09 cm

Circumference of a circle, C=2πr

\(\Rightarrow 16.09 = 2 \pi r\)

\(\Rightarrow 16.09 = 2 \times 3.14 \times r\)

\(\Rightarrow r = \frac{16.09 \times 100}{6.28 \times 100}\)

\(\Rightarrow r = 2.56 \) cm

Therefore Diameter = 2r = 2 x 2.56 = 5.12 cm.

Example 4: If the product of 38.46 and another number is 658.17, what is the other number?

Solution: Given,

One number = 38.46

Product of two numbers = 658.17

The other number = 658.17÷38.46

= \(\frac{658.17}{100}\div \frac{38.46}{100}\)

= 17.11

Example 5: Rakesh bought a new.  He went on a road trip of 165.9 km on bike. After a week he went for another trip of 102.04 km. What will be the reading on meter reader of the bike?

Solution: Given,

Distance travelled on first trip = 165.9 km

Distance travelled on second trip = 102.04km

Total distance travelled = 165.9 + 102.04 = 267.94 km

Practice Questions on Decimal Fractions

1. Write 6/1000 in decimal form.
2. What is the sum of 12/100 and 10?
3. Find the difference between 4/800 and 1/100.
4. What is the product of 18/100 and 3?

To solve more problems on the topic, download BYJU’S – The Learning App from Google Play Store and watch interactive videos. Also, take free tests to practice for exams.