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Multiplication of Decimal Numbers by 10, 100 and 1000

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Multiplication of Decimal Numbers by 10, 100, and 1000:

When a decimal number is multiplied by 10, 100, or 1000, the digits in the product are the same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.

Let us see if we can find a pattern of multiplying numbers by 10 or 100 or 1000.

  • 1.76 × 10 = `(176)/(100)` × 10 = 17.6
  • 1.76 × 100 = `(176)/(100)` × 100 = 176 or 176.0
  • 1.76 × 1000 = `(176)/(100)` × 1000 = 1760 or 1760.0

Observe the shift of the decimal point of the products.  Here the numbers are multiplied by 10, 100 and 1000. In 1.76 × 10 = 17.6, the digits are same i.e., 1, 7 and 6. The decimal point has shifted to the right by one place. Note that 10 has one zero over 1.

In 1.76 × 100 = 176.0, observe 1.76 and 176.0. The decimal point has shifted to the right by two places. Note that 100 has two zeros over one.

  • 2.35 × 10 = 23.5
  • 2.35 × 100 = 235 or 235.0
  • 2.35 × 1000 = 2350 or 2350.0

  • 12.356 × 10 = 123.56
  • 12.356 × 100 = 1235.6
  • 12.356 × 1000 = 12356.
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