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How to Convert Exponents in Metrics

The Metric system is streamlined to make unit conversions very easy. To convert from any metric prefix, for example kilometers to millimeters, simply multiply or divide by some factor of 10. Because of this, scientific notation and exponents are often used in metric conversion. Scientific notation can basically be defined as any number or unit multiplied by 10^x, with x representing the number of times to multiply or divide by 10. For example, 1 x 10^3 grams = 1 gram x (10x10x10) = 1000 g = 1 kg. Scientific notation makes converting exponents in metrics much easier.

Instructions

  1. Steps for Negative Prefixes

    • 1

      Start with a basic unit -- one liter, meter or gram.

    • 2

      Divide by 10 (10^-1 or 1/10 meter) for a decimeter, deciliter or decigram.

    • 3

      Divide the decimeter by 10 for a centimeter (10^-2 or 1/100 meter).

    • 4

      Divide a centimeter by another 10 for a millimeter (10^-3 or 1/1000 meter).

    • 5

      Divide a millimeter by another 1000 or 1 x 10^-3 for a micrometer (10^-6 or 1/1,000,000 meter).

    • 6

      Divide a micrometer by another 1,000 for a nanometer (10^-9 meter).

    • 7

      Multiply the positive exponent by 10^x, to convert from a positive prefix. "x" is the difference of the positive and negative exponent. For example, to convert a kilometer (1x10^3 meters) to a centimeter (1x10^-2 meters), subtract the positive exponent by the negative (3-(-2)=5) and multiply the positive exponent by 10^(value of the difference). When multiplying exponents, the values of the two exponents are added: 1x10^3 x 10^5 = 1x1-^(3+5) = 1x10^8, so one kilometer (1x10^3 meters) is equal to 1x10^8 cm.

    Steps for Positive Prefixes

    • 8

      Start with a basic unit -- one liter, meter, or gram.

    • 9

      Multiply by 10 (10^1 or 10 meters) for a dekameter.

    • 10

      Multiply a dekameter by 10 for a hectometer (10^2 or 100 meters).

    • 11

      Multiply a hectometer by 10 for a kilometer (10^3 or 1000 meters).

    • 12

      Multiply a kilometer by 1000 (10^3) for a megameter (10^6 or 1,000,000 meters).

    • 13

      Multiply a megameter by another 1000 for a gigameter (10^9 meters).

    • 14

      Multiply a gigameter by another 1000 for a terameter (10^12 meters).

    • 15

      Divide the positive exponent by 10^x to convert from a negative prefix. "x" is the difference of the positive and negative exponent. For example, to convert a centimeter (1x10^-2 meters) to a kilometer (1x10^3 meters), subtract the positive exponent by the negative (3-(-2)=5) and divide the negative exponent by 10^(value of the difference). When dividing exponents, the values of the two exponents are subtracted: 1x10^-2 / 10^5 = 1x10^(-2-5)=1x10^-7, so one centimeter (1x10^-2 meters) is equal to 1x10^-7 kilometers.

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