(2) An alternate method is to express the original number in scientific

notation. The power of ten in the expression is the characteristic of the original number.

The number 20 when expressed in scientific notation is 2.0 X 101. Hence, the

characteristic of the original number is one.

Both methods for determining the characteristic may be used for numbers

less than or greater than one.

b. **By Rule.**

(1) Original numbers greater than one. If the number whose logarithm is

being determined is greater than one, the characteristic for the logarithm of that number

will be positive and one less than the number of digits found to the left of the decimal

point in the original number. For example:

Original

Number of digits

Characteristic

Number

to left of decimal

(digits - one)

2.0

1

0

20.0

2

1

200.0

3

2

2000.0

4

3

20000.0

5

4

(2) Original numbers that are less than one. If the number whose logarithm

is being determined is less than one, the characteristic for the logarithm of that number

will be negative and is a number one more than the number of zeros to the right of the

decimal point that precede the first nonzero integer. For example:

Original

Number of zeros

Characteristic

Number

to right of decimal

(num. of 0 + 1)

0.2

0

-1

0.02

1

-2

0.002

2

-3

0.0002

3

-4

(3) A negative characteristic may be distinguished from a positive

characteristic by placing a negative sign above the characteristic. This is necessary

since the mantissa is always positive. For example:

_

log 0.2 = 1.3010

MD0837

1-31

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