Significant Figure Rules
Significant Figure Rules
Significant figure rules are really "rules of thumb" for how to handle the results of calculations so as not to introduce or lose precision in performing a mathematical operation. These rules are not always correct for all situations. However, in most cases, following the significant figure rules will yield a good result.
Rules concerning zero
A zero between two significant figures is significant. The number 203.2 consists of four significant figures.
A Zero to the right of a digit beyond the decimal point is a significant figure. The number 14.720 consists of five significant figures. (Note the zero would not be necessary to set the decimal point, thus it is significant).
A zero is not significant if it merely fixes the decimal point. The number 0.031 contains two significant figures, the zero sets the decimal point and is not significant. In the number 1200 the zeros may or may not be significant.
The digits and zeros shown in the decimal part of standard exponential numbers are significant.
3.2 x 10-2 indicates two significant figures.
1.2 x 103 indicates two significant figures.
1.20 x 103 indicates three significant figures.
1.200 x 103 indicates four significant figures.
Addition or Subtraction
When adding or subtracting the last digit that is retained in the sum or difference corresponds to the least precise number used in the computation.
To add: 1) Add the numbers 2) round the sum to the lowest common digit.
Ex. 5.71 g
3.222 g
+ 1276. g
----------------
1276.932 g ~ 1277 g
Multiplication or Division
When multiplying or dividing the product or quotient should contain no more digits than the least number of significant figures in the number involved in the computation.
Ex. (0.4222)(0.11) = 0.046442 = 0.046 (two significant figures)
Rules of Rounding Unnecessary Figures
Rule 1. The last significant figure is rounded up if it is followed by digits greater than five.
ex. Rounded
Significant figure rules are really "rules of thumb" for how to handle the results of calculations so as not to introduce or lose precision in performing a mathematical operation. These rules are not always correct for all situations. However, in most cases, following the significant figure rules will yield a good result.
Rules concerning zero
A zero between two significant figures is significant. The number 203.2 consists of four significant figures.
A Zero to the right of a digit beyond the decimal point is a significant figure. The number 14.720 consists of five significant figures. (Note the zero would not be necessary to set the decimal point, thus it is significant).
A zero is not significant if it merely fixes the decimal point. The number 0.031 contains two significant figures, the zero sets the decimal point and is not significant. In the number 1200 the zeros may or may not be significant.
The digits and zeros shown in the decimal part of standard exponential numbers are significant.
3.2 x 10-2 indicates two significant figures.
1.2 x 103 indicates two significant figures.
1.20 x 103 indicates three significant figures.
1.200 x 103 indicates four significant figures.
Addition or Subtraction
When adding or subtracting the last digit that is retained in the sum or difference corresponds to the least precise number used in the computation.
To add: 1) Add the numbers 2) round the sum to the lowest common digit.
Ex. 5.71 g
3.222 g
+ 1276. g
----------------
1276.932 g ~ 1277 g
Multiplication or Division
When multiplying or dividing the product or quotient should contain no more digits than the least number of significant figures in the number involved in the computation.
Ex. (0.4222)(0.11) = 0.046442 = 0.046 (two significant figures)
Rules of Rounding Unnecessary Figures
Rule 1. The last significant figure is rounded up if it is followed by digits greater than five.
ex. Rounded