# Multiplication of a Decimal by a Decimal

The topic deals with multiplication of a decimal number by another decimal number. For multiplying two decimal numbers we first need to ignore the decimal point in both the numbers and do the multiplication as we do it in case of whole numbers. After completing the multiplication then we would count the places after decimal point in the multiplier and multiplicand. Suppose if the sum of the number of places after the decimal point in the multiplier the multiplicand is 5 then leave 5 places from the left in the answer and put the decimal point to get the final answer.

Steps for multiplication of a decimal by another decimal:

Step I: First multiply both the numbers ignoring the decimal point

Step II: Then count the no. of places after the decimal in the multiplier and multiplicand

Step III: If the sum of no. of places after the multiplier and multiplicand is 3 and in the answer or product we will leave 3 places from the left to place the decimal point.

For example:

Multiply 2.32 by 1.5

We will multiply 232 by 15 ignoring the decimal point. Now no. of places after decimal point in the multiplicand is 2 and the no. of places after the decimal point in the multiplier is 1. So sum of no. of places after the multiplier and multiplicand is 3. Hence, from left we will leave 3 places to put the decimal point and the answer is 3.480

Here are few more examples to illustrate multiplication of a decimal by a decimal number.

1. Multiply 4.56 by 0.1

Solution:

Multiply 456 by 1 (ignoring the decimal point)there are 2 places at the right after the decimal in multiplicand and 1 place after the decimal in the right in the multiplier. Hence in the answer we will leave 2+1 = 3 places from the right to place decimal point.

The answer will be 0.456 after placing decimal point

2. Multiply 63.25 by 1.02

Here both the multiplicand and multiplier has two places after the decimal point in the right. Hence the sum of no. of decimal places in multiplicand and multiplier is 4 so in the answer we will leave 4 places from the right and would place the decimal point.

3. Multiply 159.45 by 2.03

Here we can see that sum of the no. of decimal places in the multiplier is 2 and in the multiplicand is 2. So, the sum of no. of decimal places in multiplier and multiplicand is 4. Hence in the product we will also leave 4 places from the right and place the decimal point.

4. Multiply 6.52 by 8.9

We can see that the no. of decimal places in the multiplicand is 2 and the no. of decimal places in the multiplier is 1. Hence the sum of the no. of decimal places in the multiplier and multiplicand is 3. Hence, in the product we need to leave 3 places from the right and put the decimal point.

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