DECIMALS TO FRACTIONS - METHOD OF CONVERTING WITH SOLVED EXAMPLES AND EXERCISE

Please study fractions and

Decimals before Decimals to Fractions,

if you have not already done so.

That knowledge is a prerequisite here.

Also study Decimal Place Value Chart.

Having a thourough knowledge of decimals
and the place value of the digits in it
helps to understand the reasoning behind
the method going to be described here.

The method is easy to follow.

But remember that, simple things need perfection
and perfection is not a simple thing.

Study the examples and solve all the problems
given in exercise and check with the Answers.

Method of Converting Decimals to Fractions

Method for decimal numbers with whole number part '0' :

Step 1 :
Remove the decimal point and write the
resulting number as the numerator.

Step 2 :
Place as many zeroes after 1 as there are places in the decimal part and write it as the denominator.

Step 3 :
Reduce the fraction thus formed to
lowest terms.









Method for decimal numbers with whole number part other than '0':

Write the decimal as whole number + decimal part.

For the decimal part, apply the method given above
to get a proper fraction.

The whole number plus this proper fraction
which is a mixed fraction is the required answer.

Solved Examples on converting Decimals to Fractions

Convert each of the following decimals
into a fraction with lowest terms.

1. 0.7
2. 0.25
3. 1.501
4. 3.075
5. 0.002
6. 8.005
7. 0.786
8. 25.06
9. 120.042
10. 27.6

Solution :

1. 0.7 = 7⁄10. Ans.
2. 0.25 = 25⁄100 = 25¹⁄100⁴ = 1⁄4. Ans.
3. 1.501 = 1 + 0.501 = 1 + 501⁄1000 = 1  ⁵⁰¹⁄₁₀₀₀. Ans.
4. 3.075 = 3 + 0.075 = 3 + 75⁄1000 = 3 + 75³⁄1000⁴⁰ = 3  ³⁄₄₀. Ans.
5. 0.002 = 2⁄1000 = 2¹⁄1000⁵⁰⁰ = 1⁄500. Ans.
6. 8.005 = 8 + 0.005 = 8 + 5⁄1000 = 8 + 5¹⁄1000²⁰⁰ = 8  ¹⁄₂₀₀. Ans.
7. 0.786 = 786⁄1000 = 786³⁹³⁄1000⁵⁰⁰ = 393⁄500. Ans.
8. 25.06 = 25 + 0.06 = 25 + 6⁄100 = 25 + 6³⁄100⁵⁰ = 25  ³⁄₅₀. Ans.
9. 120.042 = 120 + 0.042 = 120 + 42⁄1000 = 120 + 42²¹⁄1000⁵⁰⁰ = 120  ²¹⁄₅₀₀. Ans.
10. 27.6 = 27 + 0.6 = 27 + 6⁄10 = 27 + 6³⁄10⁵ = 27  ³⁄₅. Ans.

Exercise on converting Decimals to Fractions

Convert each of the following decimals
into a fraction with lowest terms.

1. 3⁄10
2. 7⁄100
3. 3⁄4
4. 13⁄200
5. 8.5
6. 27.6
7. 6.05
8. 9.375
9. 3.15
10. 27.28

Answers to Exercise on converting Decimals to Fractions

1. 0.3
2. 0.07
3. 0.75
4. 0.065
5. 8  ¹⁄₂
6. 27  ³⁄₅
7. 6  ¹⁄₂₀
8. 9  ³⁄₈
9. 3  ³⁄₂₀
10. 27  ⁷⁄₂₅