Implied Limits

numbers it is significant. For example, 1.095 has four significant figures.

(3)

Zeros appearing at the end of a number.

(a) If a number contains a decimal point and the last number (digit) is a

zero, the zero is a significant figure. For example, 15.60 has four significant figures.

(b) If the last digit in the number is a zero and the number does not

contain a decimal point, the zero may or may not be significant. For example, the

number 1670 has four significant figures if the accuracy of the measurement included

the zero as a significant digit. If the digit seven was estimated, then the zero is not

significant and hence the number contains only three significant figures.

NOTE:

For all course work that follows, any trailing zeros will be considered

significant. For example, the number 1000 has four significant figures.

c. Examples.

Number of significant

Number

figures

18.0

108

0.0018

0.0108

180

3 (for this subcourse)

1-28. IMPLIED LIMITS

If a laboratory result is reported as 3.6, it indicates that this value is accurate to

the nearest tenth and that the exact value lies between 3.55 and 3.65.

1-29. LABORATORY APPLICATION

The real importance of significant figures lies in their application to fundamental

laboratory calculations.

a. Addition and Subtraction. When adding or subtracting, the last digit

retained in the sum or difference should correspond to the first doubtful decimal place of

the addends (least accurate number).

Example. Add 5.683 plus 0.0052.

Solution. In the number 5.683, the three is the doubtful decimal place; i.e.,

the value of this measurement could vary from 5.6825 to 5.6835. Since the fourth digit

after the decimal point is unknown, the answer is limited to four digits. Thus,

5.683

+ 0.0052

5.6882 ----> 5.688

b. Multiplication and Division. When multiplying or dividing, the product or

MD0837

1-27