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How Do You Multiply Two Numbers Using Scientific Notation?

Carry out the following multiplication: 0.0000004 • 3,250,000,000

Summary

  1. '0.0000004' and '3,250,000,000' are in decimal notation
  2. '4 x 10-7' is the scientific notation version of '0.0000004'
  3. '3.25 x 109' is the scientific notation version of '3,250,000,000'
  4. Use the associative property to group similar numbers together
  5. The product of powers rule allows us to add exponents

Notes

    1. '0.0000004' and '3,250,000,000' are in decimal notation, and can be intimidating to work with
    1. This will put the numbers into a form that's easier to work with
    1. Since the decimal was moved 7 places to the right, we have a '-7' for the exponent in '4 x 10-7'
    2. Since the decimal was moved 9 places to the left, we have a '9' for the exponent in '3.25 x 109'
    1. We can do this since we are multiplying by every number
    1. The '4' comes from '4 x 10-7', and '3.25' comes from '3.25 x 109'
    1. The '10-7' comes from '4 x 10-7', and '109' comes from '3.25 x 109'
    1. Notice they each have a base of '10', which allows us to add the exponents
    2. A base is a number or variable that is raised to a power
    1. The '4' comes from '4 x 10-7', and '3.25' comes from '3.25 x 109'
    2. The '10-7' comes from '4 x 10-7', and '109' comes from '3.25 x 109'
    1. 13 x 102 = 1300