Multiplication of numbers expressed in scientific notation (cont)

b. Example. Multiply 3.2 X 102 by 2.0 X 103

Solution. Remember that when multiplying exponential expressions, the digit

terms are multiplied in the usual manner and the exponents of the exponential terms are

added, therefore:

(3.2 X 102) X (2.0 X 103) = 3.2 X 2.0 X 102 X 103 =

3.2 X 2.0 X 102+3 = 6.4 X 105

c. Example. Multiply 3.2 X 10-2 by 2.0 X 103

Solution.

(3.2 X 10-2) X (2.0 X 103) = 3.2 X 2.0 X 10-2 X 103 =

6.4 X 10-2+3 = 6.4 X 101

Equivalently:

3.2 X 10-2

Multiply the digit terms

2.0 X 103

and add the exponents of the

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exponential terms.

6.4 X 101

d. Example. Multiply 0.00056 by 0.013 using scientific notation.

Solution. Before you multiply, the above numbers must be converted to

scientific notation. Multiply the digit terms and add the exponentential terms.

Thus, 0.00056 = 5.6 X 10-4 and 0.013 = 1.3 X 10-2

5.6 X 10-4

1.3 X 10-2

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7.28 X 10-6 ----> 7.3 X 10-6

MD0837

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