The idea of significant figures is that when you’re doing work in physics or chem class, you’re taking measurements – and any good measurement is precise. Measurements have limited precision, which means that the results of your calculations also have limited precision. Significant figures (or “sigfigs”) are a method of tracking and calculating measurement precision.
Calculating Significant Figures:
1) Any non-zero number is a significant figure. 6.345, for example, has four sig figs. 3.1415 has 5 sig figs
2) Expressing measurements as "powers" are not significant. 10^3 = Insignificant. 10^1000 = Insignificant.
3) A zero in between any two numbers is always significant. 134063 = 6 sig figs. 1044.605 = 7 sig figs
4) A zero on the left of a measurement in never significant because they only act as place holders for the number. Example, 0.0024 can also be written at 2.4 x 10^ -3, so there are only 2 sig figs. 0.00000000000000001 = 1 sig fig.
5) Seeing if zeros to the right of the measurement are significant or not all depends on their position in relation to the decimal point. Example, if there isn't one - zeros are never significant (100 = 1 sig fig, 550 000 = 2 sig figs).
If there is one, however, the zeros do in fact become significant. Zeros that appear to the right of a decimal/ other digits after the decimal are significant, such as 5.340, because they represent the accuracy to which the decimal was measured.
Zeros that are to the right of a number before the decimal point are also significant (5000. = 4 sig figs, 6390.01 =6 sig figs).
2) Expressing measurements as "powers" are not significant. 10^3 = Insignificant. 10^1000 = Insignificant.
3) A zero in between any two numbers is always significant. 134063 = 6 sig figs. 1044.605 = 7 sig figs
4) A zero on the left of a measurement in never significant because they only act as place holders for the number. Example, 0.0024 can also be written at 2.4 x 10^ -3, so there are only 2 sig figs. 0.00000000000000001 = 1 sig fig.
5) Seeing if zeros to the right of the measurement are significant or not all depends on their position in relation to the decimal point. Example, if there isn't one - zeros are never significant (100 = 1 sig fig, 550 000 = 2 sig figs).
If there is one, however, the zeros do in fact become significant. Zeros that appear to the right of a decimal/ other digits after the decimal are significant, such as 5.340, because they represent the accuracy to which the decimal was measured.
Zeros that are to the right of a number before the decimal point are also significant (5000. = 4 sig figs, 6390.01 =6 sig figs).
Significant Figures in Operations:
Addition / Subtraction : Round the answer to the least number of decimal places. Ex) 55.55 + 8.779 = 64.33
136.03 - 24.3 = 111.7
Multiplication / Division : Round your answer to the least number of sig figs. This means your answer should have the same amount of sig figs as the measurement being multiplied/divided with the lowest number sig figs.
Ex) 6.0 (2 sf) x 5.55 (3 sf) = 33 (2 sf)
144144.0 (7 sf) / 12.0 (3 sf) = 1.20 x 10^4
*When doing multiple operations of the same operation (dimensional analysis), don't calculate sig figs for each operation, wait until you have your final answer in order to keep the full precision until the end.
**When doing multiple operations of different operations (area), the rule must apply separately and you must calculate sig figs for each operation.
136.03 - 24.3 = 111.7
Multiplication / Division : Round your answer to the least number of sig figs. This means your answer should have the same amount of sig figs as the measurement being multiplied/divided with the lowest number sig figs.
Ex) 6.0 (2 sf) x 5.55 (3 sf) = 33 (2 sf)
144144.0 (7 sf) / 12.0 (3 sf) = 1.20 x 10^4
*When doing multiple operations of the same operation (dimensional analysis), don't calculate sig figs for each operation, wait until you have your final answer in order to keep the full precision until the end.
**When doing multiple operations of different operations (area), the rule must apply separately and you must calculate sig figs for each operation.