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Mr. Baldwin Mathematics & Measurement PHYSICS 9/17/2013 Aim: Why are significant figures important? (What is precision and accuracy?) Do Now: How many seconds are there in a year? Convert you answer to scientific notation and round it off to 2 decimal places. Homework: SWBAT Distinguish between accuracy and precision. Determine the precision of measured quantities Significant Figures reviewed The number of significant figures is the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written. Some Examples: 23.21 cm has 4 significant figures 0.062 cm has 2 significant figures (the initial zeroes don’t count) 80 km is ambiguous – it could have 1 or 2 significant figures. If it has 3, it should be written 80.0 km. EXAMPLE: A meter-stick is used to measure a pen and the measurement is recorded as 14.3 cm. This measurement has three valid digits: two you are sure of, and one you estimated. The valid digits in a measurement are called significant digits. However, the last digit given for any measurement is the uncertain digit. How many significant digits are in these measurements? a) 25.001 cm ________ b) 0.00012 kg ________ c) 35,000 m/s ________ d) 5.611 x 105 s ________ e) 0.0120 mm ________ f) 2.00 x 10-3 mL ________ g) 750 dg ________ Operations Involving Significant Figures When multiplying or dividing numbers, the result has as many significant figures as the number used in the calculation with the fewest significant figures. Example: 11.3 cm x 6.8 cm = 77 cm When adding or subtracting, the answer is no more accurate than the least accurate number used. CHECK! Can you create ONE example each of addition and subtraction involving sig. figs.? Check! Which of the following representations is correct when you solve 0.030 kg + 3333 g using scientific notation? A. 3.4×103 g B. 3.36×103 g C. 3×103 g D. 3363 g Accuracy & Precision Define accuracy and precision? OR Create two sentences each using the words precision and accuracy • Accuracy is the proximity of measurement results to the true value • Precision, the repeatability, or reproducibility of the measurement Section Check Read the following question and justify who gets the most accurate and precise value Ronald, Kevin, and Paul perform an experiment to determine the value of acceleration due to gravity on the Earth (980 cm/s2). The following results were obtained: Ronald: 961 ± 12 cm/s2, Kevin: 953 ± 8 cm/s2, and Paul: 942 ± 4 cm/s2. . A. Kevin got the most precise and accurate value. B. Ronald’s value is the most accurate, while Kevin’s value is the most precise. C. Ronald’s value is the most accurate, while Paul’s value is the most precise. D. Paul’s value is the most accurate, while Ronald’s value is the most precise. Answer: C Reason: Ronald’s answer is closest to 980 cm/s2, hence his result is the most accurate. Paul’s measurement is the most precise, it’s within 4 cm/s2. The precision of a measurement is one-half of the smallest division of the instrument. Formulate your OWN question • Each person is to come up with a similar question(s) and have the person in front or behind you answer your question(s). • In the measurement, 86.21, the “2” is (certain, estimated) and (significant, not significant). The “1” is (certain, estimated) and (significant, not significant).