Multiplying Decimals

Multiplication of decimals, is similar to multiplying the numbers without considering the decimal points. The placement of the decimal point on the product is very crucial in order to get the correct place value of the digits.


 Steps for Multiplying Decimals

  •  Multiply the numbers without considering the decimal points.
  •  Add the decimal places to the right-hand side of the decimal point in both factors. The sum should be the number of decimal places in the product starting from its last digit.


Decimal Multiplication Example


Example 1:
 7.85

Explanation:

Multiply the numbers without considering the decimal points.

  3 1 4
×   2 5
1 5 7 0
6 2 8  
7 8 5 0

Add the decimal places in both factors.
`3.14` `- 2` decimal places
`2.5` `- 1` decimal places
The decimal point of the product should be 2 + 1 = 3 decimal places from the left of the last digit.
Move the decimal point 3 places to the left starting from the right of the last digit of the product which is 0.
`7.850 or 7.85`
Therefore, `3.14 × 2.5 = 7.85`


Example 2:
 97.1232

Explanation:

Multiply the numbers without considering the decimal points.

    8 0 4  
  × 1 2 0 8
  `1` 6 4 3 2
  1 6 0 8
8 0 4
9 7 1 2 3 2

Add the decimal places in both factors.
`8.04 - 2` decimal places
`12.08 - 2` decimal places
The decimal point of the product should be 2 + 2 = 4 decimal places from the left of the last digit.
Move the decimal point 4 places to the left starting from the right of the last digit of the product which is 0.
`97.1232`
Therefore, `8.04 × 12.08 = 97.1232`






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