The concept to remember is when doing math, the answer is only as good as your worst estimate. Here a YouTube video explaining how to multiply and divide numbers while following the rules of significant figures.
Calculate the number of significant digits in each number.
Multiply and divide all the numbers without rounding any numbers -ever. Write down this answer.
Round the final answer to the FEWEST number of significant digits of the numbers being multiplied.
Logarithms and Significant Figures
The number of significant figures in the lagged number is equal to the number of significant figures after the decimal of the answer.
This is because the number to the left of the decimal, (called the "characteristic,") in the answer is the power of ten.
log(2512) = 3.4000 ...Four s.f. in the number. Four digits after the decimal in the answer.
log(212) = 2.326 ...Three s.f. in the number. Three digits after the decimal in the answer.
...Five s.f. in the number. Five digits after the decimal in the answer.
Calculate the answer for each expression according to the rules of significant figures.
34.5 x 3.4
6000 x 3
102 x 5.677
45.2 / 24
45 x 3.04
35 x 0.04
900 x 2.45
0.983 x 12
0.34 x 0.206
34 / 300
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)