1.6 – Calculating with Significant Figures

Rules for using significant figures in calculations: Adding and subtracting: keep the least number of decimal places (or place values) to the right in the answer.

Rules for using significant figures in calculations: For example, adding 1.000 g and 2.5 g gives 3.5 g. Other examples: 34.07 + 4.810 = 38.880 becomes 38.88 because 34.07 only has two decimal places 100. + 78.33 + 2.4 = 180.73 becomes 181 because 100. has no decimals but a significant ones place   110 + 25.0 = 135.0 becomes 140 because 110 does not have a decimal and does not have a significant ones place so answer must round to tens place. Since the 5 will be eliminated, look at it and round up

Practice Problems: 23.5 + 10.234 = 33.734 rounded to 33.7 23.5 + 10.234 = 33.734 rounded to 33.7 543 - 123.367 = 419.633 rounded to 420.

Rules for using significant figures in calculations: Multiplying and dividing: keep the least number of significant figures in the answer.

Rules for using significant figures in calculations: For example, 3.0000 m  4.00 m gives 12.0 m2. Examples: 3.2 x 2.76 = 8.832 but will become 8.8 because 3.2 only has two sig figs; look at the 3 since it is eliminated and it will not round   10 x 3.9854 = 39.854 but becomes 40 because 10 only has one sig fig.; look at 9 since it is eliminated and round up

Practice Problems: 4.6 x 1.023 = 4.7058 rounded to 4.7 1500 / 250.10 = 5.9976 rounded to 6.0

Rules for using significant figures in calculations: Averaging: when averaging, the average cannot be more accurate than the data collected. For example, average 9.75g, 9.59 and 9.83. The sum is 29.17 which follows sig fig rules since all three numbers have two decimal places. Divided by 3 and it = 9.723. The answer becomes 9.72 since my avg cannot be more accurate than the original data

Practice Problem (Hint – remember the order of operations!):   20.489 kg ÷ (900 m2 – 547 m2) x (200. s + 87.63 s) =353  400 =287.63  288 (900 does not have (200. does not have a decimal a significant ones but does have a significant ones place or tens place so so answer rounds to ones place) answer must round to hundreds place) 20.489 ÷ 400 x 288 = 14.752 becomes 10 because 400 only has one sig fig so the answer can only have one sig fig.