DIVIDING DECIMALS - METHODS OF DIVIDING WITH SOLVED EXAMPLES AND EXERCISE

Please study Long Division before Dividing Decimals

if you have not already done so.

The knowledge of the method of Dividing
whole numbers with long division presentation
is a prerequisite here. Once you master Dividing
whole numbers, the methods described here,
are easy to follow.

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

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

Dividing Decimals by 10, 100, 1000 etc.

When a decimal number is divided by 10, the
decimal point moves to the left by one place.

When a decimal number is divided by 100, the
decimal point moves to the left by two places.

When a decimal number is divided by 1000, the
decimal point moves to the left by three places.

and so on.

Thus, we observe :

When a decimal number is divided by numbers like 10, 100,
1000...., the decimal point in the given decimal number moves as
many places to the left as the number of zeros in the divisor.
If there are not enough (adequate) places on the left side,
we keep '0' s in those places and keep the decimal point.

Examples :

1. 9.62 ÷ 10 = 0.962 ( decimal point shifted 1 place to the left )
2. 1.13 ÷ 10000 = 0.000113 ( decimal point shifted 4 places to the left )
3. 6.9732 ÷ 1000 = 0.0069732 ( decimal point shifted 3 places to the left )
4. 0.01 ÷ 100 = 0.0001 ( decimal point shifted 2 places to the left )
5. 999999 ÷ 100000 = 9.99999 ( decimal point shifted 5 places to the left )

Dividing Decimals by Whole Number

Step 1 :
Perform the Division of the decimal number
by the whole number in the usual manner.

Step 2 :
When the division of whole number part of the
dividend is complete, put the decimal point
in the quotient and proceed with the division
as in case of whole numbers.

Continue the process
till the remainder is zero. Add zeros to the
extreme right end of the dividend, if required.

Example on Dividing Decimal by Whole Number

Find 79.865 ÷ 8.

Solution :

                Dividend
 Divisor   8 )   79.865000   ( 9.983125   Quotient    
                 72
                 -----
                  78
                  72    
                 -----  
                   66 
                   64   
                 ----- 
                    25
                    24
                 ----- 
                     10 
                      8   
                     ----- 
                      20 
                      16
                     ----- 
                       40
                       40
                     ----- 
                        0  Remainder
                     ----- 

Dividing Decimal by Decimal

Step 1 :
Convert the divisor into a whole number by multiplying
the dividend and the divisor by a suitable power of 10.
Step 2 :
Now divide the new dividend by the whole number
so obtained as explained above.

Example on Dividing Decimal by Decimal

Find 0.00216 ÷ 0.27

Solution :
0.00216 ÷ 0.27 = (0.00216 x 100) ÷ (0.27 x 100)
= 0.216 ÷ 27

                Dividend
 Divisor   27 )   0.216   ( 0.008   Quotient    
                  0
                 -----
                  02
                   0    
                 -----  
                   21 
                    0   
                 ----- 
                   216
                   216
                 ----- 
                     0 Remainder
                 -----

Exercise on Dividing Decimals

Find the values of :

1.  
   1. 1452 ÷ 100
   2. 975318 ÷ 100000
   3. 987.5 ÷ 1000
   4. 0.08 ÷ 10
   5. 0.7 ÷ 10000
2.  
   1. 281.25 ÷ 15
   2. 21.568 ÷ 32
3.  
   1. 2.3358 ÷ 0.17
   2. 0.8085 ÷ 0.35

For Answers, see at the bottom of the page.

Answers to Exercise

1.  
   1. 14.52
   2. 9.75318
   3. 0.9875
   4. 0.008
   5. 0.00007
2.  
   1. 18.75
   2. 0.674
3.  
   1. 13.74
   2. 2.31