Chapter 2 Significant Figures and Meaningful Data 1Chapter 2(S 20)SIGNIFICANT FIGURES AND MEANINGFUL DATASignificant figures is the standard method used to round off an answer. Rounding off should NEVER interfere with solving a problem, and should only be considered after solving the problem. The rounded number indicates how important a number is, how much trust we can have in the number. The more significant figures or digits, the more trust we have in the number. A number with only a few significant figures is not very trustworthy. SIGNIFICANT FIGURES AND UNCERTAINTY Significant figures are all measured digits in a reported number.This includes all reported integers. For example, 34.56 mm contains four significant figures. Confusion may be encountered when the integer is 0, which occurs one out of ten times. For example, 34.560 mm contains five significant figures. The last zero was reported because it was measured and is thus significant. In contrast, 0.03456 mm contains four significant figures since the first two zeros are used only to show where the decimal place is. Putting such a number into scientific notation clears up any confusion, 3.456 x 10-2mm clearly contains four significant figures. The last significant figure in a number contains uncertainty but is still significant.Uncertainty is the +/- in a reported number.Uncertainty is found in the last significant figure and is understood to exist even if no one mentions it. For example, the uncertainty in 34.56 mm occurs in the hundreds place and is designated as ±0.01 mm, or in scientific notation as 1 x 10-2mm. How you write the number conveys information about how much trust you can put into the number. More significant figures and smaller uncertainty correlate with more trust. When you examine the following examples you will learn that 200.00 mm is a more trustworthy number than 200 mm:number uncertainty meaning # sig figs 200.00 mm ±0.01 mm 199.99 mm, 200.00 mm, or 200.01 mm 5 200.0 mm ±0.1 mm 199.9 mm, 200.0 mm, or 200.1 mm 4 200. mm ±1 mm 199 mm, 200. mm, or 201 mm 3 200 mm ±100 mm 100 mm, 200 mm, or 300 mm 1 Notice the difference in meaning between 200. mm and 200 mm. Without the terminal decimal point, 200 mm is considered an almost useless number. If a person doesn’t know about the meaning of the decimal point and left it out, his number will be interpreted in the most conservative manner and would be taken as insignificant or unworthy. How would you show 200 m with 2 significant figures ? Here are four methods: _ i. 200 m, with the line over non-significant placeholders ii. 20(0) m, with the parenthesis indicating non-significant integers iii. 2.0 x 102 m, scientific notation leaves no doubt about the number of significant figures iv. 200 m ±10 m, the uncertainty indicates which are significant Here are some examples using small numbers: number uncertainty meaning # sig figs 0.2 m ±0.1 m 0.1 m, 0.2 m, or 0.3 m 1 0.002 m ±0.001 m 0.001 m, 0.002 m, or 0.003 m 1 0.0020 m ±0.0001 m 0.0019 m, 0.0020 m, or 0.0021 m 2 0.0002020 m ±0.0000001 m 0.0002019 m, 0.0002020 m, or 0.0002021 m 4
Chapter 2 Significant Figures and Meaningful Data 2Uncertainty can be displayed in the same way as the number itself, or put into scientific notation.