Fractions to Decimals, Decimals to Fractions - Orchids The International School
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Decimals

Conversion: Fractions to Decimals, Decimals to Fractions

  • 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.
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Method to convert fractions to 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

2 / 5
to the decimal.

Solution:

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

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

Boy

Therefore,

2 / 5
= 0.4

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

3 / 4
to decimal using the long division method

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.
Boy

Therefore,

3 / 4
= 0.75

Method to convert decimals to fractions

  • 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

4 / 100
.

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