Having a thourough knowledge of decimals
and the place value of the digits in it
helps to understand the reasoning behind
the methods going to be described here.
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 Fractions to Decimals
Simple method : Fractions to Decimals
This method is suitable when the
denominator is a power of 10.
This method is simply putting a decimal point
in the Numerator by looking at the denominator.
When the denominator is a power of 10,
count the number of zeros in it (say 'n').
Then the required decimal is obtained by
putting a decimal point in the numerator
after 'n' digits from the right.
If there are not sufficient number
of digits, put zeros.
Examples :
19⁄10 = 1.9
7⁄1000 = .007 = 0.007
234⁄100 = 2.34
56789⁄1000 = 56.789
9786412⁄100000 = 97.86412
Sometimes, we can convert a fraction to an
equivalent fraction with denominator, a power of 10.
Then, we can apply the simple method.
Examples :
3⁄20 = (3x5)⁄(20x5) = 15⁄100 = .15 = 0.15
7⁄4 = (7x25)⁄(4x25) = 175⁄100 = 1.75
13⁄50 = (13x2)⁄(50x2) = 26⁄100 = 0.26
5⁄8 = (5x125)⁄(8x125) = 625⁄1000 = 0.625
1⁄250 = (1x4)⁄(250x4) = 4⁄1000 = 0.004
Long Division Method : Fractions to Decimals
This is a general method and
can be used for any fraction.
Step 1 :
Perform the usual long division with numerator
as dividend and denominator as divisor till we
get a remainder (which is less than the divisor).
Step 2 :
Put a decimal point in the dividend and the quotient.
Step 3 :
Put a zero on the right of the decimal point in the
dividend as well as on the right of the remainder.
Divide again just as whole numbers.
Step 4 :
Repeat step 3 till the remainder is zero.
The quotient is the required decimal.
The method will be clear by the following examples.
Example 1 is an Improper Fraction,
Example 2 is a mixed fraction
and Example 3 is a proper fraction.
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Convert the following fractions into decimals by simple method
13⁄10
693⁄100
29⁄10000
9856⁄1000
9731⁄100000
9⁄5
7⁄20
8⁄125
11⁄40
1⁄16
Convert the following fractions into decimals by division method
35⁄8
37⁄40
16 3⁄8
1 9⁄16
6 9⁄32
For Answers, see at the bottom of the pages.
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