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# Significant Figures, Decimal Places, and Rounding Part I

Part I Introduction and Rules for Determining Significant Figures and Decimal Places

One of the key parts of presenting numerical results in a consistent way is the use of significant figures, commonly abbreviated as “sig figs,” and decimal places. This three- part post will focus on the basics for determining the number of sig figs and decimal places, rules for rounding and recommendations for how many sig figs or decimal places should be reported.

Significant Figures Rules

First, the easy rule:

All non-zero results are considered significant.

Examples:

19 has two sig figs, 35.2 has three sig figs.

The rules for determining if 0 is significant are presented below.

When working with whole numbers only:

Zero is significant if it is between any two other sig figs; this applies to multiple 0s as well.

Trailing 0s in a number may be either significant or insignificant, but can be identified with underlining to indicate the last sig fig in the number. Placing a bar over the last sig fig is also used, but is not as readily available in standard word processor or spreadsheet programs.

Examples:

101 has three sig figs, and 1001 has four sig figs.

2000 has an indeterminate number of sig figs, which could range from one to four sig figs. If the number is instead reported as 2000, then the sig figs have been fixed at two.

The rules for determining whether 0 is significant in a decimal value are:

If the number to the left of the decimal point is 0, then all leading 0s before the first non-zero value are insignificant, all 0s between non-zero values are significant, and all trailing 0s are also significant.

If the absolute value of the number to the left of the decimal point is 1 or greater, then all 0s to the right of the decimal point are significant. Any 0s immediately to the left of the decimal point are also significant.

Examples:

0.0123 has three sig figs.

0.01230 has four sig figs.

1.0123 has five sig figs.

1.012030 has seven sig figs.

10.0123 has six sig figs.

The number of decimal places is defined as the total number of digits to the right of the decimal point. In the above examples, the number of decimal places would be 4, 5, 4, 6, and 4 respectively. Reporting to a specific number of sig figs or decimal places is commonly used when presenting results.

Using standard scientific notation will remove any ambiguity from trailing 0s in a whole number. In the example above in which 2000 was used, the number would be presented as 2.0 X 103 in scientific notation, and the rules for determining sig figs apply only to the number before the exponent multiplier (103 in this example).