Rounding and Significant Digits - Basic Mathematics for Water and Wastewater Operators - page 105

5 Rounding and

Significant Digits

The significant figures of a number are those digits that carry meaning, contributing
to its precision. However, although the number of significant figures roughly corre-
sponds to precision, it does not correspond to accuracy.

ROUNDING NUMBERS
When rounding numbers, the following key points are important:

1. Numbers are rounded to reduce the number of digits to the right of the deci-
mal point. This is done for convenience, not for accuracy.

2. Rule: A number is rounded off by dropping one or more numbers from the
right and adding zeros if necessary to place the decimal point. If the last
figure dropped is 5 or more, increase the last retained figure by 1. If the last
digit dropped is less than 5, do not increase the last retained figure.

■ Example 5.1
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

DETERMINING SIGNIFICANT FIGURES
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.

Note: No answer can be more accurate than the least accurate piece of data used
to calculate the answer.

3. Rule: Significant figures are those numbers that are known to be reliable.
The position of the decimal point does not determine the number of signifi-
cant figures.

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