7 UncertaintiesThe percent error is how far off your own measurement or calculation is from the correct value.
8 Question:What value should you record as the length of the beetle? Explain your answer. (The ruler is showing cm)
9 Significant FiguresSignificant figures are the digits in a measurement that are known for certain, plus one uncertain digit.As scientists, we do not care about any digits that are not significant.When we take measurements in lab we only report significant figures.
10 Significant FiguresIn the example, we are certain that the beetle is at least 1.5 cm in length, but the hundredths place is uncertain.We would therefore report this value as 1.55The one and five are certain digitsThe second five is uncertain (depending on your opinion, you might report this as 1.54 or 1.56 – these would also be correct)Therefore, this measurement has three total significant figures (two certain digits and one uncertain digit)
12 Significant Figures How to determine significant figures: All nonzero digits are significant.Interior zeros (zeros between two nonzero numbers) are significant.Trailing zeros (zeros to the right of a nonzero number) that fall after a decimal point are significant.
13 Significant FiguresTrailing zeros that fall before a decimal point are significant.Leading zeros (zeros to the left of the first nonzero number) are NOT significant. They serve only to locate the decimal point.Trailing zeros at the end of a number with no decimal point are NOT significant.
14 Significant FiguresExact numbers are not counted as significant figures.Exact counting of discrete objectsNumbers that are part of an equationDefined quantities (e.g. a dozen, a mole, etc)Some conversion factors are defined quantities, while others are not.1 in. = 2.54 cm exact
15 Significant Figures 0.0035 1 dozen = 12 1.080 100.00 2371 100,000 How many significant figures are in each number?0.00351 dozen = 121.080100.002371100,0002.9 × 105
16 Significant Figures Rules for Rounding: When numbers are used in a calculation, the result is rounded to reflect the significant figures of the data.For calculations involving multiple steps, round only the final answer—do not round off between steps.This practice prevents small rounding errors from affecting the final answer.
17 Significant FiguresRound down if the last digit dropped is 4 or less; round up if the last digit dropped is 5 or more.
18 Significant Figures Round to 3 sig-figs: 4.287 4.29
19 Significant Figures Multiplication and Division Rule: The result of multiplication or division carries the same number of significant figures as the factor with the fewest significant figures.
20 Significant FiguresThe intermediate result (in blue) is rounded to two significant figures to reflect the least precisely known factor (0.10), which has two significant figures.
21 Significant FiguresThe intermediate result (in blue) is rounded to three significant figures to reflect the least precisely known factor (6.10), which has three significant figures.
22 Significant Figures Addition and Subtraction Rule: In addition or subtraction calculations, the result carries the same number of decimal places as the quantity carrying the fewest decimal places.
23 Significant FiguresWe round the intermediate answer (in blue) to two decimal places because the quantity with the fewest decimal places (5.74) has two decimal places.
24 Significant FiguresWe round the intermediate answer (in blue) to one decimal place because the quantity with the fewest decimal places (4.8) has one decimal place.
25 Significant FiguresIn calculations involving both multiplication /division and addition/subtraction:do the steps in parentheses firstdetermine the correct number of significant figures in the intermediate answer without roundingthen do the remaining steps.
26 Significant Figures 3.489 × (5.67 – 2.3) 3.489 × 3.37 = 11.758 = 12 do the step in parentheses first – 2.3 = 3.37Use the subtraction rule to determine that the intermediate answer has only one significant decimal place. To avoid small errors, it is best not to round at this point; instead, underline the least significant figure as a reminder.3.489 × 3.37 = = 12Use the multiplication rule to determine that the intermediate answer (11.758) rounds to two significant figures (12) because it is limited by the two significant figures in 3.37.
27 Significant Figures 56.55 × 0.920 ÷ 34.2585 Perform each calculation to the correct number of significant figures.56.55 × ÷
28 Significant Figures 1.10 × 0.512 × 1.301 × 0.005 ÷ 3.4 Perform each calculation to the correct number of significant figures.1.10 × × × ÷ 3.4
29 Significant FiguresPerform each calculation to the correct number of significant figures.
30 Significant FiguresPerform each calculation to the correct number of significant figures.
31 Significant Figures 6.78 × 5.903 × (5.489 – 5.01) Perform each calculation to the correct number of significant figures.6.78 × × (5.489 – 5.01)
32 Significant Figures 3.897 × (782.3 – 451.88) Perform each calculation to the correct number of significant figures.3.897 × (782.3 – )
33 Significant Figures 3 + (15/12) (3 + 15)/12 Which calculation would have its result reported to the greater number of significant figures?3 + (15/12)(3 + 15)/12