Intro - 2 - Significant Figures | Lecture Note

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High School Physics
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2024
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0.2 Significant Figures Why Significant Figures? 1. 2. Measurement cannot exceed level of precision (extra digits have no meaning). Indicates the level of confidence you have in your measurement or answer. 1 Significant Figures: (Sig figs) 1. All “non-zero” digits are significant. Eg. 25.1 = 3 sig. figs. 2. Zeros used solely to place the decimal are not significant. Eg. 0.000025 = 2 sig. figs. 3. Zeros between two other significant figures are significant. Eg. 0.0205 = 3 sig. figs. 4. Trailing zeros (to the right of the decimal) that are not needed to place the decimal are significant. Eg. 0.02500 = 4 sig. figs. Sig. Figs continued 5. Addition and subtraction operations are significant to least precise decimal place. 6. Division and multiplication operations are significant to the lowest # of sig figs of all factors being multiplied or divided. 7. When doing calculations, round only once at the end. That is, keep the # on the calculator, or write down at least 4 dec. places as you go. Details Appendix 4 p396-p399. 15 Exact Numbers • Integers, exact rational fractions, or mathematical constants do not limit the number of sig figs in the answer (eg 2, 10, ¼, π, e) ALL numbers that are multiples of 10 (ie 2000) must be written in scientific notation (1 non-zero digit, then decimal point and decimal places as needed) to be accurate. eg. 2 x 103 indicates 1 significant figure. 2.0 x 103 indicates 2 significant figures 2.00 x 103 indicates 3 significant figures 2.000 x 103 indicates 4 significant figures Rounding - Any number is only rounded once, not more. - Ex: round 149 to nearest 100. - Answer is 100… do not round 9 up to make 150 and then around 150 up to make 200. The following method is commonly used: – Perform the calculation without any rounding (save intermediate answers in your calculator). – Round your final answer to the same precision as the least precise value in the given data. – Express your answer in scientific notation if necessary. Addition example eg. What is the perimeter of a rectangle with sides of 12.1 cm and 4.64 cm ? 12.1 cm 12.1 cm 4.64 cm +4.64 cm 33.48 cm But “12.1” is significant to the 1st decimal place while “4.64” to the 2nd dp. So the answer is expressed to the 1st dp because it is the least precise. 33.48 cm becomes 33.5 cm. Multiplication example eg. What is the area of an object that is 41.2 cm x 7.8 cm ? 41.2 x 7.8 = 321.36 cm2 But “7.8” only has two sig figs. So the answer can only have two sig figs. 321.36 cm2 becomes 320 cm2 or 3.2 x 102 cm2 Mixed example! eg. What is the speed of an object given by the following formula: V = 5.50 m/s + 0.00125 m/s2 * 15 s 0.00125 m/s2 * 15 s = 0.01875 m/s But “15” only has two sig figs. Therefore, the product can only have two sig figs. We will NOT round at this step, but we note that product would round to 0.019, which has three dp. Mixed example! We have now finished all multiplication steps and are left with V = 5.50 m/s + 0.01875 m/s Now we follow the rule for addition, which is the least precise dp (2nd place). V = 5.51875 m/s , which becomes 5.52 m/s Trig example Trigonometry follows multiplication rules Ex. Vx = 12 m/s * cos(35.2°) Vx = 9.805739 m/s, becomes 9.8 m/s Ex. Vy = 1875 m/s * sin(15°) Vy = 485.29 m/s, becomes 4.9 x 102 m/s Each rounded to 2 sig figs because that is the lowest # of sig figs in each problem. Obtain Assignment #1