Basic Math & Pre-Algebra For Dummies
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Multiplying numbers that are in scientific notation is fairly simple because multiplying powers of ten is easy. Here's how to multiply two numbers that are in scientific notation:

  1. Multiply the two decimal parts of the numbers.

    Suppose you want to multiply the following: (4.3 x 105)(2 x 107)

    Multiplication is commutative, so you can change the order of the numbers without changing the result. And because of the associative property, you can also change how you group the numbers. Therefore, you can rewrite this problem as (4.3 x 2)(105 x 107).

    Multiply what's in the first set of parentheses — 4.3 x 2 — to find the decimal part of the solution: 4.3 x 2 = 8.6.

  2. Multiply the two exponential parts by adding their exponents.

    Now multiply 105 x 107: 105 x 107 = 105 + 7 = 1012

  3. Write the answer as the product of the numbers you found in Steps 1 and 2.

    8.6 x 1012

  4. If the decimal part of the solution is 10 or greater, move the decimal point one place to the left and add 1 to the exponent.

    Because 8.6 is less than 10, you don't have to move the decimal point again, so the answer is 8.6 x 1012.

    Note: This number equals 8,600,000,000,000.

This method works even when one or both of the exponents are negative numbers. For example, if you follow the preceding series of steps, you find that (6.02 x 1023)(9 x 10–28) = 5.418 x 10–4. Note: In decimal form, this number equals 0.0005418.

About This Article

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About the book author:

Mark Zegarelli is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he’s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.

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