Division of numbers expressed in scientific notation

1-24. DIVISION OF NUMBERS EXPRESSED IN SCIENTIFIC NOTATION

a. Method One. To divide exponential expressions, the digit term of the

numerator is divided by the digit term of the denominator in the usual way, and the

exponent of the denominator is subtracted from the exponent of the numerator.

(1)

Example. Divide 103 by 102

Solution. In division, the exponent of the denominator is subtracted from

the exponent of the numerator. Therefore:

103 divided by 102 = 103-2 = 101 = 10

(2)

Example. Divide 5.0 X 103 by 2.5 X 102

Solution. By using method one, the laboratory specialist divides 5.0 by

2.5 and then subtracts the exponents of the exponential terms. Therefore:

5.0

----= 2.0 and 103-2 = 101

2.5

Thus, 5.0 x 103 divided by 2.5 X 102 = 2.0 X 101

b. Method Two. In this method of dividing exponential expressions, the digit

term is treated in exactly the same manner as in method one. The exponential term in

the denominator is moved to the numerator, with the appropriate sign change, and the

exponents of the exponential terms in the numerator are added.

(1)

Example. Divide 5.0 X 103 by 2.5 X 102

Solution.

5.0 X 103

5.0 X 103 X 10-2

5.0 X 103-2

-------- = ---------------- = ------------ = 2.0 X 101

2.5 X 102

2.5

(2)

Example. Divide 0.000005 by 250

Solution. Before the above numbers can be divided using the methods

previously demonstrated, they must be converted to scientific notation.

Thus, 0.0000050 = 5.0 X 10-6 and 250 = 2.5 X 102

5.0 X 10-6

5.0 X 10-6 X 10-2

---------- = ---------------- = 2.0 X 10-8

2.5 X 102

2.5

MD0837

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