Conversions: Fractions to Decimals, Decimals to Fractions

Decimal to Fraction for Class 5 Math

From the concept of decimal to fraction, students can convert a decimal number to a fraction number and a fraction number to a decimal number.

In this learning concept, the students will learn

• The application of how to convert decimals into a fraction and how to convert fractions into decimals.
• To evaluate fractions to decimals and decimals to fractions.

Each concept is explained to class 5 maths students using illustrations, examples, and mind maps. Students can assess their learning by solving the two printable worksheets given at the page’s end.

Download the decimal-to-fraction worksheet for class 5 and check the solutions to the decimal-to-fraction provided in PDF format.

• A fraction is the number expressed as the numerator divided by the denominator.
• Example: 2/3, 5/2, etc.
• A decimal is the number in which the whole number part and the fractional part are expressed together.
• Example: 0.523, 1.978, etc.

             

 How to Convert Fractions Into Decimals?

• By converting the denominator to the power of 10, i.e., 10, 100, 1000, etc.
• Long division method.

Converting the Denominator to the Power of 10

• Think about the number which when multiplied by the denominator gives the number that is in the power of 10.
• Multiply the numerator and the denominator of the fraction by that number.
• Count the number of zeros in the denominator and place the decimal from the right hand of the numerator and then remove the denominator.
• Insert 0 at the left of the numerator if it has fewer digits.

Example:

Convert the fraction

Solution:

Step 1: We know that 5 × 2 = 10. Therefore, multiply the numerator and the denominator of the given fraction by 2.

Step 2: The denominator has 1 zero. Place a decimal point after one digit.

Therefore,

Long Division Method

• Divide the numerator by the denominator.
• Put a decimal point in the quotient directly above the decimal point in the dividend.
• Add 0 in the dividend if required to complete the division.

Example:

Convert the fraction

Solution:

• Consider 3 as the dividend and 4 as the divisor.
• Since 4 > 3. Put 0 above 3 in the quotient and then place a decimal point.
• Add 0 after 3. Now consider the number as 30.
• We know 4 × 7 = 28. Write 28 below 30 and 7 in the quotient.
• Subtract 28 from 30 to get 2.
• Put 0 after 2 and consider the number as 20.
• We know 4 × 5 = 20. Write 20 below 20 and 5 in the quotient.
• Subtract 20 from 20 to get 0.

Therefore,

                 

How to Convert Decimals Into a Fraction?

• Observe the number of digits after the decimal point.
• The denominator of the fraction will be in the power of 10. The number of zeros will be the same as the number of digits after the decimal point.
• The numerator of the fraction will be the numbers in decimal.

Example:

Convert the decimal 0.04 to the fraction.

Solution:

The given decimal has 2 digits after the decimal point. Therefore, the denominator of the equivalent fraction will be 100.

The numerator will be 4.

Therefore, the equivalent fraction is