# Multiplication of Decimal Numbers

This topic would deal with multiplication of decimal numbers. Previously in case of addition and subtraction we have seen that we need to change the set of decimal numbers to be added or subtracted into like decimal fractions but here changing into like decimal fraction is not required. Here we need to multiply two decimal numbers as we multiply whole numbers without considering the decimal point. After finding out the product count the number of decimal places in both the numbers (i.e. the multiplicand and the multiplier) and in the result also counts as many places from the last place towards the right to place the decimal point.

Steps of multiplication of decimal numbers:

Step I: Multiply both the numbers as we multiply in whole numbers.

Step II: Then count the number of places after decimal in multiplier and multiplicand and place the decimal point leaving the same no. of places from the left in the final answer

Here are few examples on multiplication of decimal numbers:

1. Multiply 87.95 by  9

Solution:

8  7  .  9  5

×              9

7   9  1  .  5  5

Here as we multiply in case of whole numbers we will multiply first 9 with 5 to get 45 but we will only write 5 and 4 will be carried over. Then in tenths place 9 is multiplied with 9 to get 81 and 4 carrying from hundredths place to make it 85 in the tenths place and we will write 5 and 8 would be carried over to the units place. Now 9 multiplied by 7 is 63 and carry 8 would make it 71 and hence would write 1 and 7 carrying. Now 9 multiplied by 8 is 72 and 7 carry would make it 79. As in the  multiplicand the no. of decimal place is 2 all together. The decimal will be placed leaving 2 places from the left of the number.

2. Multiply 40.62 by 2.3

Solution:

4  0 . 6  2

×        2 . 3

1  2  1  8  6

8  1  2  4   0

9  3 . 4  2  6

Here as we multiply in case of whole numbers we will multiply first 3 with 2 to get 6 and then 3 with 6 to get 18 where 8 is written and 1 carried over.  Again 3 is multiplied by 0 to get 0 and 8 carry over hence will write 8. Again 3 is multiplied with 4 to get 12. In the second row  2 is multiplied with 2 to get 4 and then 2 is multiplied with 6 to get 12 but we will only write 2 with 1 carrying. For the units place 2 is multiplied with 0 to get 0 and 1 is carried over and hence will write 1 and finally 2 is multiplied with 4 to get 8. The decimal will be placed leaving 3 places from the left of the number. As in the multiplier and multiplicand the no. of decimal place is 3 all together.

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