How to Divide Decimals

Dividing decimals is similar to dividing whole numbers, only difference is we have to handle the decimal point before start dividing. To divide decimals, move the decimal points in the divisor and dividend to the right to make the divisor a whole number. Place a decimal point in the quotient directly above where the decimal point appears in the dividend. Dividing is the most challenging of four basic mathematical operations. Dividing decimals is almost the same as dividing whole numbers, except use the position of the decimal point in the dividend to determine the decimal places in the result.

Division with Decimals

While dividing the decimals, move the decimal points of the divisor and dividend as many places to the right to make the divisor a whole number. When dividing a decimal by a whole number, it is not necessary to move the decimal points of the either the divisor or the dividend. In such cases add zeros to the right of the dividend only. When dividing decimal fractions, the value of the answer is not changed if the decimal points of the divisor and the dividend are moved the same number of places to the right. It is same as multiplying both divisor and dividend by the same number.

Steps for Dividing Decimals:

Step 1: Make the divisor a whole number, for that move the decimal point of the divisor as many places to the right.

Step 2: Move the decimal point of the dividend same number of the places as were divisor moved.

Step 3:
Write the decimal point in the quotient above the decimal point in the dividend.

Step 4: Add zeros to the dividend if necessary.

Step 5: Divide as with whole numbers.

Solved Examples

Question 1: Divide 4.21 by 0.014. Round the answer to 2 decimal places.

Solution:
Given,  4.21 $\div$ 0.014

Step 1:

Move the decimal points 3 places to the right in the divisor and dividend.

=> 4210.0 $\div$ 14.0

Step 2:

Place the decimal point of the quotient directly above the decimal point of the dividend.

           3 0 0 .  7 1 4
       _____________
14  | 4 2 1 0 . 0
      - 4 2
      -----------------
       0 0   1 0 0
            -     9 8
     ---------------------
                   0 2 0
                 -    1 4
     -----------------------
                       0 6 0
                   -      5 6
     ----------------------------
                          0 4
     ----------------------------

=> 4210.0 $\div$ 14.0 = 300.714 = 300.71 (approx)

 

Question 2: Divide 89.235 by 0.25
Solution:
Given,  89.235 $\div$ 0.25

Step 1:
Move the decimal points 3 places to the right in the divisor and dividend.

=> 89.235 $\div$ 0.25

Step 2:
Place the decimal point of the quotient directly above the decimal point of the dividend.

             3 5 6 . 9 4
         _____________
2 5  |  8 9 2 3 . 5
      -   7 5
      -----------------
          1 4 2
       -  1 2 5
     ---------------------
           0 1 7 3
        -     1 5 0  
     -----------------------
               0 2 3 5
           -      2 2 5
     ----------------------------
                   0 1 0 0
            -         1 0 0
     ----------------------------
                         x
     ----------------------------

=>  89.235 $\div$ 0.25 = 3 5 6 . 9 4

 

Dividing Decimals

To divide a decimal, first place a decimal point in the quotient above the decimal point in the dividend. If needed add a zero to hold a place. If there is no decimal point in the dividend or dividend is a whole number, add a zero to the dividend for each place value after the decimal point in the divisor. To divide a decimal by a whole number usually we use long division. The decimal point in the answer is placed directly above the decimal point in the dividend. When divide the decimals, change the divisor to a whole number by moving the decimal point to the right as many places as necessary move the decimal point in the dividend the same number of places.

Solved Examples

Question 1: Divide 43.23 $\div$ 5.8

Solution:
Given, 43.23 $\div$ 5.8

Step 1:
To write the divisor as a whole number, multiply the numerator and denominator by 10

=> $\frac{43.23 * 10}{5.8 * 10} = \frac{432.3}{58}$

Step 2:
Place the decimal point of the quotient directly above the decimal point of the dividend.



=> 43.23 $\div$ 5.8 = 7.45

 

Question 2: Divide 0.45398 by 0.56

Solution:
Step 1:
Move the decimal points 2 places to the right in the divisor and dividend

=> 45.36 $\div$ 56

Step 2:
Divide as with whole numbers



=> 45.36 $\div$ 56 = 0.8106