Decimal Multiplication by Power of 10

Multiplying decimal numbers by 10, 100, 1000……

Multiply any decimal by any power of 10 or 10, 100, 1000, we just move the decimal point towards the right as many places as the number of zeros in the power of 10.

When we multiply any decimal by 10, we move the decimal point one place to the right.

When we multiply any decimal by 100, we move the decimal point two place to the right.

Similarly, we multiply any decimal by 1000, we move the decimal point three place to the right.

Example: 85.6 x 100

100 has two zeros, so we will move two places to the right to the decimal point. Therefore, the result is

85.6 x 100 = 856

Example: 43.8 x 1,000

Here, 3 zeros in 1,000, so, move the decimal point in 43.8 to the right 3 places.

43.8 x 1000 = 43,800

43.8 x 1000 = 43,800

Example:

93.542 x 10 = 935.42,

93.542 x 100 = 9354.2,

93.542 x 1,000 = 93,542,

93.542 x 10000 = 935,420

Multiply decimals by power of 10

10¹ = 10

10² = 100

10³ = 1000

Example: let’s see a example

43.542 x 10¹ = 435.42

Here exponent is 1, so, move 1 place to the right to the decimal point.

43.542 x 10² = 4354.2

Here exponent is 2, so, move 2 places to the right to the decimal point.

43.542 x 10³ = 43,542

Here exponent is 3, so, move 3 places to the right to the decimal point.

43.542 x 10⁴ = 435,420

Here exponent is 4, so, move 4 places to the right to the decimal point.

Each zero in the power of 10, move the decimal point one place to the right.

Example 1: Multiplying  1.98 x 10

1.98 x 10 move the decimal point 1 place to the right.

Solution: 1.98 x 10 = 19.8

Example 2: Multiplying  25.732 x 100

Solution: 25.732 x 100 move the decimal point 2 place to the right.

25.732 x 100 = 2573.2

Example 3: Multiplying  0.04 x 100

Solution: 0.04 x 100 move the decimal point 2 place to the right.

0.04 x 100 = 4

Example 4: Multiplying  0.003 x 100

Solution: 0.003 x 100 move the decimal point 2 place to the right.

0.003 x 100 = 0.3

Example 5: Multiplying  23.451x 1000

Solution: 23.451 x 1000 move the decimal point 3 place to the right.

23 .451 x 1000 = 23451

Example: 6 Multiplying  0.0065 x 10,000

Solution: 0.0065 x 10,000 move the decimal point 4 place to the right

0.0065 x 10000 =65

Example 7: Multiplying  3.74 x 110

                            110 = 11 x 10

                         3.74 x 110 = 3.74 x 11 x 10

                        3.74 x 110 = 3.74 x 10 x 11

                           3.74 x 10 = 37.4

                           = 37.4 x 3.74 x 110 = 411.4