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Recognize powers of 10

Powers of 10 represent repeated multiplication of 10 by itself: 101=1010^1=10, 102=10010^2=100, 103=1,00010^3=1{,}000, and so on; the exponent indicates the number of factors of 10, and for positive whole-number exponents the value has a corresponding pattern of zeros. This structure connects exponential notation to place value and multiplying or dividing by 10, 100, or 1,000; negative and fractional exponents and powers of bases other than 10 are not included.

Detailed Explanation: Recognize powers of 10

A power of (10)(10) shows how many times to multiply (10)(10) by itself. The small raised number is the exponent.

For positive whole-number exponents:

  • (101=10)(10^1=10): one factor of (10)(10)
  • (102=10×10=100)(10^2=10\times10=100): two factors of (10)(10)
  • (103=10×10×10=1,000)(10^3=10\times10\times10=1{,}000): three factors of (10)(10)

The exponent also tells you how many zeros come after the 11.

Example: Find (104)(10^4).

  1. The exponent is 44, so use four factors of (10)(10):
104=10×10×10×1010^4=10\times10\times10\times10
  1. Count four zeros after the 11:
104=10,00010^4=10{,}000

So, 104=10,000\boxed{10^4=10{,}000}.

Remember: for a positive whole-number power of (10)(10), the exponent tells you the number of zeros.

Learn by doing: Recognize powers of 10

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    Powers of Ten - Calculation

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