Basic Math Operations - Mathematics and Statistics for the Environment - page 46

RULE
Significant figures are those numbers that are known to be reliable. The position of the deci-
mal point does not determine the number of significant figures.
■ EXAMPLE 2.13
Problem: Round off the following numbers to one decimal.
Solution:
34.73 = 34.7
34.77 = 34.8
34.75 = 34.8
34.45 = 34.4
34.35 = 34.4
■ EXAMPLE 2.14
Problem: Round off 10,546 to 4, 3, 2, and 1 significant figures.
Solution:
10,546 = 10,550 to 4 significant figures
10,546 = 10,500 to 3 significant figures
10,546 = 11,000 to 2 significant figures
10,547 = 10,000 to 1 significant figure
When determining significant figures, the following key points are important:
1. The concept of significant figures is related to rounding.
2. It can be used to determine where to round off.
Key Point: No answer can be more accurate than the least accurate piece of data used to calculate
the answer.
■ EXAMPLE 2.15
Problem: How many significant figures are in a measurement of 1.35 in.?
Solution: Three significant figures: 1, 3, and 5.
■ EXAMPLE 2.16
Problem: How many significant figures are in a measurement of 0.000135?
Solution: Again, three significant figures: 1, 3, and 5. The three zeros are used only to place the
decimal point.
■ EXAMPLE 2.17
Problem: How many significant figures are in a measurement of 103,500?
Solution: Four significant figures: 1, 0, 3, and 5. The remaining two zeros are used to place the
decimal point.