Significant Figures

Rules for SigFigs Any non-zero digit is significant Any trapped zeros are significant Zeros before the decimal point at the end of a number are NOT significant (trailing zeros) Zeros after the decimal point at the beginning of a number are NOT significant (leading zeros) Trailing zeros after the decimal ARE significant Answer can have only as many sigfigs as the fewest in the problem

EXAMPLES 23 – both are non-zero numbers (2 sigfigs) 109 – zero between two non-zero numbers (trapped zero – 3 sigfigs) 4500 – trailing zeros before the decimal are NOT significant (2 sigfigs) 0.000785 – leading zeros after the decimal are NOT significant (3 sigfigs) 6.00 – trailing zeros after the decimal ARE significant (3 sigfigs)

SigFigs and Calculations Adding/Subtracting Use fewest number of decimal places Rounding rules apply Multiplying/Dividing Use fewest number of sigfigs

Scientific Notation Can be only 1 number to the left of the decimal Second part is written as (x 10n) If the number to be written is smaller than 1 then n MUST be negative If the number to be written is larger than 1 then n MUST be positive

EXAMPLES Write the following in scientific notation: 157 – move decimal two places to left 1.57 x 102 23000 – move decimal four places to left 2.3 x 104 0.0000279 – move decimal five places to right 2.79 x 10-5 0.000000000324 – move decimal ten places to right 3.24 x 10-10