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

Please study fractions and

Decimals before Fractions to Decimals,

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 methods going to be described here.

Also knowledge of Long Division

is a prerequisite here.

The methods are 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 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 :

1. 19⁄10 = 1.9
2. 7⁄1000 = .007 = 0.007
3. 234⁄100 = 2.34
4. 56789⁄1000 = 56.789
5. 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 :

1. 3⁄20 = (3x5)⁄(20x5) = 15⁄100 = .15 = 0.15
2. 7⁄4 = (7x25)⁄(4x25) = 175⁄100 = 1.75
3. 13⁄50 = (13x2)⁄(50x2) = 26⁄100 = 0.26
4. 5⁄8 = (5x125)⁄(8x125) = 625⁄1000 = 0.625
5. 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.

Example 1 of Long Division Method : Fractions to Decimals

Convert 37⁄8 as decimal by long division method.

Solution :

                 Dividend
 Divisor   8 )    37.000     ( 4.625   Quotient
                  32
                  ----
                   50
                   48
                  ----
                    20
                    16
                  -----
                     40
                     40
                    -----  
                      0  Remainder   
                    ----- 

Example 2 of Long Division Method : Fractions to Decimals

Convert 5  ¹⁄₄₀ as decimal by long division method.

Solution :
5  ¹⁄₄₀ = (5x40 + 1)⁄40 = 201⁄40

                  Dividend
 Divisor   40 )    201.000     ( 5.025   Quotient
                   200
                  ----
                     10
                      0
                    ----
                     100
                      80
                     -----
                      200
                      200
                     -----
                        0  Remainder 
                     -----
                     
                      

Example 3 of Long Division Method : Fractions to Decimals

Convert 9⁄32 as decimal by long division method.

Solution :

                  Dividend
 Divisor   32 )    9.00000     ( 0.28125   Quotient
                   0
                  ----
                   90
                   64
                  ----
                   260
                   256
                  -----
                     40
                     32
                    -----  
                      80   
                      64  
                     -----
                      160
                      160
                     -----
                        0  Remainder
                     -----

Exercise on Converting Fractions to Decimals

1. Convert the following fractions into decimals by simple method
   1. 13⁄10
   2. 693⁄100
   3. 29⁄10000
   4. 9856⁄1000
   5. 9731⁄100000
   6. 9⁄5
   7. 7⁄20
   8. 8⁄125
   9. 11⁄40
   10. 1⁄16
2. Convert the following fractions into decimals by division method
   1. 35⁄8
   2. 37⁄40
   3. 16  ³⁄₈
   4. 1  ⁹⁄₁₆
   5. 6  ⁹⁄₃₂

For Answers, see at the bottom of the pages.

Answers to Exercise

1.  
   1. 1.3
   2. 6.93
   3. 0.0029
   4. 9.856
   5. 0.09731
   6. 1.8
   7. 0.35
   8. 0.064
   9. 0.275
   10. 0.0625
2.  
   1. 4.375
   2. 0.925
   3. 16.375
   4. 1.5625
   5. 6.28125