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Home >> Decimal >> Multiplication of Decimals >> Multiplication of Decimal with 10, 100, 1000, 10000 >>

Multiplication of Decimal with 10, 100, 1000, 10000

Properties Multiplication of Decimals Multiplication of a decimal with another decimal Multiplication of decimal with a whole number Multiplication of Decimal with 10, 100, 1000, 10000



Before you understand this topic, you are advice to read:

Define Decimal Point ?
Define Multiplicand ?
Define Multiplier ?

To understand this concept, study the following example:

Example 1: Multiply 23.5678 with 10

Solution : Multiply 23.5678 with 10 and we get:
23.5678 X 10 = 235.678

Now compare the multiplicand and the product:
You can see that digits in multiplicand and product are same. And the difference is only that decimal point is shifted to the right by one place.

Example 2: Multiply 23.5678 with 100
Solution: Multiply 23.5678 with 100 and we get:
23.5678 X 100 = 2356.78

Now compare the multiplicand and the product:
Here again, you can see that digits in multiplicand and product are same. And the difference is only that decimal point is shifted to the right by two places.

From example 1 and example 2, we have two following observations:

  • 1. Observation 1: In both the examples digits in multiplicand and product are same. And the difference is only shifting of decimal point to the right.

  • 2. Observation 2: Number of places decimal point shifts is equal to the number of zero(s) in the multiplier i.e.

    In Example 1: decimal point shifted one place and multiplier (10) has one zero
    In Example 2: decimal point shifted two places and multiplier (100) has two zeros.

    Hence, from above two observations it's concluded that:
    When a decimal is multiplied by 10 or 100 or 1000 or 10000 & so on .. The multiplicand and the product remains same and decimal point shifts to the right by as many number of places as there are number of zero(s) in the multiplier.
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