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Fractions to Decimals

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Fractions whose denominator is 10 or power of 10 can be converted to decimals by the following steps.

Step 1: Check if the denominator is 10 or power of 10. If it is not a power of 10, then multiply the denominator with a number so that the denominator can be a power of 10.

Step 2: Multiply the numerator and denominator by the same number.

Like, multiply \frac{1}{4}  by 25 in the numerator and denominator.

\frac{1}{4} =  \frac{1\times25}{4\times25}=\frac{25}{100}

Step 3: Write the number in the numerator and put the decimal point according to the number of zeroes in the denominator. For every zero put decimal one space from the right hand side.

So,  = 0.25

The fractions \frac{3}{10}  ,  \frac{8}{100} , \frac{16}{40000} are written as 0.3, 0.08, 0.0016 respectively in decimal notation.

When there is no way in which we can make the denominator a power of 10, as in the example below.

Example: Convert  \frac{4}{9}to decimal to two decimal places.

Here we can calculate an approximate decimal.

Multiply the denominator by 11 so that denominator becomes 9 × 11 = 99, which is close to 100.

\frac{4}{9}  =\frac{4\times11}{9\times11}  =\frac{44}{99}

Since 99 is close to 100, so \frac{44}{99}= 0.44 to two decimal places.

Check Point

Convert the given fractions to decimals.

  1. \frac{3}{5}
  2. \frac{387}{400}
  3. \frac{107}{200}
  4. \frac{1}{2}
  5. \frac{29}{33}(correct to two decimal places)
Answer key
  1. 0.6
  2. 0.9675
  3. 0.535
  4. 0.5
  5. 0.87
Download/Solve a Worksheet for Fractions to Decimals

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