Decimal Movement.

b. Examples.

(1)

100 = 1 X 10 X 10 = 1 X 102

In the above example, the digit term is the number one and the exponential term is ten

squared (102).

(2)

200 = 2 x 10 X 10 = 2 X 102

In this example, the digit term is the number two and the exponential term is ten

squared (102).

(3)

745 = 7.45 X 10 X 10 = 7.45 X 102

(4)

0.00486 = 4.86 X 10-1 X 10-1 X 10-1 = 4.86 X 10-3

c. Decimal Movement. In examining the above examples, it is easily seen that

the exponent of the number ten is determined by movement of the decimal point. The

exponent of the number ten is positive when the decimal is moved to the left and

negative when moved to the right. Standard scientific notation refers to the placement

of the decimal to the right of the first nonzero integer.

(1) Positive exponents. When the decimal point is moved to the left, the

exponent of the number ten is always positive.

(2) Negative exponents. When the decimal point is moved to the right, the

exponent of the number ten is always negative.

(3)

Examples.

214 = 2.14 X 102

0.102 = 1.02 X 10-1

In the first example using the number 214, the decimal was moved two

places to the left and thus the exponent of the number ten is two. In the second

example using the number 0.102, the decimal was moved one place to the right and

thus the exponent of the number ten is minus one (-1).

MD0837

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