Decimal fraction:

In a fraction, Denominators that are having a power of 10 are called the Decimal fraction. A power of 10 means 10, 100,1000, 10000 and so on. 

Example:

Convert 0.4 into decimal fractions?

To convert 0.4 into decimal fractions, simply try to write the denominator as a power of 10. This is the first step for you to look into. So let’s make the denominator as a power of 10.

We will get 4/10. This is the decimal fraction of the number 0.4.

Types of Decimal fractions:

  • Terminating Decimals: Terminating or non-recurring decimals means which do not repeat. Example: 0.76, 0.25 etc.
  • Non-terminating repeating decimals:

Decimals which are having a set of values repeating. Example: Rational numbers 0.314314314 etc.

  • Non-terminating non-repeating decimals:

These are the decimal numbers that repeat endlessly with no group of digits. 

Example: Irrational numbers ( 2)½ = 1.4142135……

Steps to convert Decimal to fraction:

Step 1: Write down the decimal number and write it in the form of a fraction that is in the form of numerator and denominator. 

Example: let the number be 0.75. Now convert this into the form of a fraction that is (75/100). That’s; this is the first step.

Step 2: Now make the denominator value reach the value of the power of 10; if the denominator value is not a power of 10. (A power of 10 means 10, 100, 1000, 10000 and so on.)

Example: let the number be ¾. Now convert the denominator value to a power of 10 which is  100 Let’s multiply 25 in both numerator and denominator so that we can get the denominator value 100.

We have; ¾ = 3 × 25 / 4 × 25 = 75/100.

Step 3: Simplify this into fractions.

For example: let 75/100 is the output of the second step. Now let’s simplify this value to a fraction we will get 3/ 4.

Some solved Questions with Decimal fractions:

Q1) Convert the following decimal into a fraction

  1. 0.25
  2. 0.04
  3. 1.2

Answer: 

  • To convert 0.25 into a fraction let’s follow the steps:

Step 1: Write the decimal number in the form of a fraction that is 25/100.

Step 2: Now make the denominator value reach the value of the power of 10; if its denominator value is not a power of 10.

We have the denominator value from step 1 is 100 (which is a power of 10). So we got 25/100. 

Step 3: Simplify this into a fraction that is 25/100 = ¼.

This is the final value formed by converting decimal value 0.25 to fraction ¼.

  • To convert 0.04 into a fraction let’s follow the steps:

Step 1: Write the decimal number in the form of a fraction that is 4/100.

Step 2: Now make the denominator value reach the value of the power of 10; if its denominator value is not a power of 10.

We have the denominator value from step 1 is 10 (which is a power of 10). So we got 4/100. 

Step 3: Simplify this into a fraction that is 4/100 = 1/25.

This is the final value formed by converting decimal value 0.04 to fraction 1/25.

  • To convert 1.2 into a fraction let’s follow the steps:

Step 1: Write the decimal number in the form of the fraction that is 12/10.

Step 2: Now make the denominator value reach the value of the power of 10; if its denominator value is not a power of 10.

We have the denominator value from step 1 is 10. So we got 12/10. 

Step 3: Simplify this into a fraction that is 12/10 = 6/5

This is the final value formed by converting decimal value 1.2 to fraction 6/5.

Steps to convert fraction Into decimal:

Step 1: Write the fraction value and make the denominator value reach the value of the power of 10; if the denominator value is not a power of 10. (A power of 10 means 10, 100, 1000, 10000 and so on.) 

Example : 5/4 = 125 / 100

Step 2: Write the decimal value.

Example: 125/100 = 1.25 (Ans)

Some solved Questions with Decimal fractions:

Q1) Convert the following fraction into decimal

  1. 5/200 litre of water
  2. 2/3 kilograms of rice

Answer:

  • To convert 5/200 litre of water into a decimal let’s follow the steps:

Step 1: Write the fraction value and make the denominator value reach the value of the power of 10; but here we have to convert to litre so let’s make the denominator value to 1000. Now 5/200 will be 25/1000.

Step 2: To write the decimal value first, 25/1000 = 0.025 litre  (Answer)

  • To convert 2/5 kg of rice into a decimal let’s follow the steps:

Step 1: Write the fraction value and make the denominator value reach the value of the power of 10; so multiplying 2 in numerator and denominator we will get,

4/10.

Step 2: To write the decimal value first, 4/10 = 0.4 kg (Answer)

Conclusion:

Now we can convert the decimal values to fraction value and fraction value to decimal value by following the steps.