Significant Figures

Rule 1: All non-zero digits are significant. Ex: 48.7 2962 = 3 SF = 4 SF

Rule 2: Zeros in the middle of a series of numbers are significant Rule 2: Zeros in the middle of a series of numbers are significant. Ex: 203 490,702 50,008 = 3 SF = 6 SF = 5 SF

Zeros in front of a series of numbers are not significant. Rule 3: Zeros in front of a series of numbers are not significant. (They are being used as place holders to insure the correct number of decimal places.) Ex: 0.008 0.473 0.0305 = 1 SF = 3 SF = 3 SF

Rule 4: Zeros to the right of a decimal are significant. Ex: 3. 00 437 = 3 SF = 6 SF = 5 SF

Rule 5: Zeros at the end of a number that are followed by a decimal are significant. Ex: 2000. = 4 SF

Rule 6: Zeros at the end of a number that does not have a decimal are not considered to be significant. (They may be significant, but we do not have enough information to be sure.) Ex: 2000 assume 1 SF

Atlantic – Pacific Rule Pacific Rule - If a decimal is PRESENT start counting with the first non-zero digit from the left. Pacific Side: decimal present 0.0019 65.01 0.0300 700. Atlantic Side: decimal absent 80200 400000 32105 700 2 SF 3 SF 4 SF 1 SF 3 SF 5 SF 3 SF 1 SF Atlantic Rule – If the decimal is ABSENT start counting with the first non-zero digit from the right.

Rules for doing calculations The answer to a set of calculations can not be more accurate than the least accurate value used in the calculation.

Multiplication and Division The number of significant figures in the answer is equal to the lowest number of significant figures used in the calculation. Ex 1: 20.7 x 8.436 = 174.652 this will be reported with 3 SF as 175 Ex 2: 8.340/4.2 = 1.985712 this will be reported with 2 SF as 2.0

Addition and Subtraction Use the same number of decimal places as the least accurate value. (smallest number of decimal places) Ex 1: 49.1 + 8.001 = 57.101 This will be reported as 57.1 Ex 2: 240 – 71.3 = 168.7 Round to the tens place and report as 170