Fraction as Decimal

We will discuss how to express fraction as decimal.


Fractions with denominator 10:

Fractional Number       Fraction           Decimal

        9 tenths                    \(\frac{9}{10}\)                      0.9

        6 tenths                    \(\frac{6}{10}\)                      0.6

        3 tenths                    \(\frac{3}{10}\)                      0.3

        7 tenths                    \(\frac{7}{10}\)                      0.7

      27 tenths                    \(\frac{27}{10}\)                      2.7

There

is

only 1 zero in the

denominator, hence

1

decimal place.


Fractions with denominator 100:

Fractional Number       Fraction           Decimal

     3 hundredths               \(\frac{3}{100}\)                   0.03

   28 hundredths                \(\frac{28}{100}\)                  0.28

 368 hundredths               \(\frac{368}{100}\)                   3.68

4192 hundredths              \(\frac{4192}{100}\)                 41.92

There

are

2 zeros in the

denominator, hence

2

decimal places.


Fractions with denominator 1000:

Fractional Number       Fraction           Decimal

      9 thousandths             \(\frac{9}{1000}\)                0.009

    19 thousandths             \(\frac{19}{1000}\)                0.019

  319 thousandths             \(\frac{319}{1000}\)                0.319

3812 thousandths             \(\frac{3812}{1000}\)                3.812

There

are

3 zeros in the

denominator, hence

3

decimal places.


To convert fractions to decimals, remember the following steps.

Step I: Write the mixed fraction as an improper fraction.

Step II: Then write the numerator.

Step III: Count the number of zeroes in the denominator. The number of decimal places is equal to the number of zeroes in the denominator.

Step IV: Put the decimal point counting the number of digits from the right equal to the number of zeroes in the denominator.

Step V: If the number of digits in the numerator is less than the number of zeroes in the denominator, put the required number of zeroes between the decimal point and the number so that the decimal place equals the number of zeroes.


Let us consider some of the following examples on expressing a fraction as a decimal.

1. Convert \(\frac{4}{5}\) into a decimal.

Solution:

\(\frac{4}{5}\) can be written as \(\frac{4 × 2}{5 × 2}\)

                          = \(\frac{8}{10}\)

                          = 0.8

We multiply the numerator and the denominator by 2 to make the denominator 10.


2. Convert \(\frac{3}{25}\) into a decimal.

Solution:

\(\frac{3}{25}\) can be written as \(\frac{3 × 4}{25 × 4}\)

                          = \(\frac{12}{100}\)

                          = 0.12

We multiply the numerator and the denominator by 4 to make the denominator 100.


3. Convert 2\(\frac{3}{5}\) into a decimal.

Solution:

2\(\frac{3}{5}\) can be written as 2 + \(\frac{3}{5}\)

                          = 2 + \(\frac{3 × 2}{5 × 2}\)

                          = 2 + \(\frac{6}{10}\)

                          = 2 + 0.6

                          = 2.6


We multiply the numerator and the denominator by 2 to make the denominator 10.


4. Convert 14\(\frac{57}{250}\) into a decimal.

Solution:

14\(\frac{57}{250}\) can be written as 14 + \(\frac{57}{250}\)

                               = 14 + \(\frac{57 × 4}{250 × 4}\)

                               = 14 + \(\frac{228}{1000}\)

                               = 14 + 0.228

                               = 14.228


We multiply the numerator and the denominator by 4 to make the denominator 1000.


Questions and Answers on Fraction as Decimal:

I. Convert the following fractions to decimals:

(i) \(\frac{19}{100}\)      

(ii) \(\frac{3}{100}\)        

(iii) \(\frac{36}{10}\)       

(iv) \(\frac{145}{100}\)  

(v) \(\frac{27}{1000}\)   

(vi) \(\frac{3124}{1000}\)             

(vii) \(\frac{956}{10}\)   

(viii) \(\frac{204}{100}\)

(ix) 3\(\frac{26}{100}\)  

(x) 18\(\frac{43}{100}\)




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