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Multiply by powers of ten

Multiplying a whole number by 10n10^n, where nn is a nonnegative integer, increases its value by a factor of ten for each power and shifts every digit nn places to the left in the base-ten place-value system; for whole-number numerals, this appears as appending nn zeros, which serve as place-value placeholders rather than constituting the operation itself. This understanding connects multiplication, place value, and exponent notation and is limited here to whole numbers and nonnegative powers of ten, not negative powers, decimal factors, or scientific notation.

Detailed Explanation: Multiply by powers of ten

To multiply a whole number by a power of ten, use the exponent to determine how many places each digit moves left.

For example:

4,372×1034{,}372 \times 10^3
  1. The exponent is 33, so each digit moves 3 places to the left.
  2. Moving the digits left leaves 3 ones-placeholders, or zeros, at the end:
4,372→4,372,000 4{,}372 \rightarrow 4{,}372{,}000
  1. Therefore,
4,372×103=4,372,000 \boxed{4{,}372 \times 10^3 = 4{,}372{,}000}

The three zeros show that the digits have shifted three place-value positions left. Multiplying by 10310^3 is the same as multiplying by 1010 three times:

4,372×10×10×10=4,372,0004{,}372 \times 10 \times 10 \times 10 = 4{,}372{,}000

Learn by doing: Multiply by powers of ten

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