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Powers of 10

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Powers of 10

A series of numbers known as the powers of 10 are generated by repetitively multiplying the base number 10 by itself. Due to their use in representing very large or very small numbers, the powers of 10 are significant in both mathematics and science.

Very often, the base number (in this case, 10) is written followed by a superscript indicating the exponent when writing the powers of 10, using exponential notation (the number of times the base is multiplied by itself). For instance, the number 10,000 is represented by the fourth power of 10, which is written as 104. (10 x 10 x 10 x 10).

Below are a few examples of the powers of 10:

  • 10^0 = 1 (1 x 10^0 = 1)
  • 10^1 = 10 (1 x 10^1 = 10)
  • 10^2 = 100 (1 x 10^2 = 100)
  • 10^3 = 1,000 (1 x 10^3 = 1,000)
  • 10^4 = 10,000 (1 x 10^4 = 10,000)
  • 10^5 = 100,000 (1 x 10^5 = 100,000)

When the exponent is higher than 0, the powers of 10 can be positive; or negative, that is when the exponent is less than 0. As an example, very small numbers like the size of atoms or the distances between galaxies can be depicted by the powers of 10.

In these situations, an exponent is generally a negative number:

  • 10^-1 = 0.1 (1 x 10^-1 = 0.1)
  • 10^-2 = 0.01 (1 x 10^-2 = 0.01)
  • 10^-3 = 0.001 (1 x 10^-3 = 0.001)
  • 10^-4 = 0.0001 (1 x 10^-4 = 0.0001)
  • 10^-5 = 0.00001 (1 x 10^-5 = 0.00001)

As they make it possible to conveniently and clearly represent very large or very small numbers, the powers of 10 are a very significant concept in mathematics and science.

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