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Fraction as Decimal

We will discuss how to express fraction as decimal.


Fractions with denominator 10:

Fractional Number       Fraction           Decimal

        9 tenths                    910                      0.9

        6 tenths                    610                      0.6

        3 tenths                    310                      0.3

        7 tenths                    710                      0.7

      27 tenths                    2710                      2.7

There

is

only 1 zero in the

denominator, hence

1

decimal place.


Fractions with denominator 100:

Fractional Number       Fraction           Decimal

     3 hundredths               3100                   0.03

   28 hundredths                28100                  0.28

 368 hundredths               368100                   3.68

4192 hundredths              4192100                 41.92

There

are

2 zeros in the

denominator, hence

2

decimal places.


Fractions with denominator 1000:

Fractional Number       Fraction           Decimal

      9 thousandths             91000                0.009

    19 thousandths             191000                0.019

  319 thousandths             3191000                0.319

3812 thousandths             38121000                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 45 into a decimal.

Solution:

45 can be written as 4×25×2

                          = 810

                          = 0.8

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


2. Convert 325 into a decimal.

Solution:

325 can be written as 3×425×4

                          = 12100

                          = 0.12

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


3. Convert 235 into a decimal.

Solution:

235 can be written as 2 + 35

                          = 2 + 3×25×2

                          = 2 + 610

                          = 2 + 0.6

                          = 2.6


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


4. Convert 1457250 into a decimal.

Solution:

1457250 can be written as 14 + 57250

                               = 14 + 57×4250×4

                               = 14 + 2281000

                               = 14 + 0.228

                               = 14.228


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

Worksheet on Fraction as Decimal

Questions and Answers on Fraction as Decimal:

I. Convert the following fractions to decimals:

(i) 19100      

(ii) 3100        

(iii) 3610       

(iv) 145100  

(v) 271000   

(vi) 31241000             

(vii) 95610   

(viii) 204100

(ix) 326100  

(x) 1843100


II. Express the following fractions as decimals.

(i) 6/10

(ii) 3/10

(iii) 4/10

(iv) 8/10

(v) 14/100

(vi) 7/100

(vii) 13/100

(viii) 97/100

(ix) 27/1000

(x) 9/1000

(xi) 427/1000

(xii) 659/1000


Answer:

II. (i) 0.6

(ii) 0.3

(iii) 0.4

(iv) 0.8

(v) 0.14

(vi) 0.07

(vii) 0.13

(viii) 0.97

(ix) 0.027

(x) 0.009

(xi) 0.427

(xii) 0.659

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