What powers of 10 mean

10n10^n tells you how many times to multiply or divide by ten.

Positive exponents move the decimal point to the right. Negative exponents move it to the left.

This is the backbone of metric prefixes, scientific notation, and many scale conversions.

Examples

  • 103=100010^3=1000
  • 10−2=0.0110^{-2}=0.01
  • 100.5=sqrt1010^{0.5}=sqrt{10}

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