P2F11-Week1-Barwick-ans

# P2F11-Week1-Barwick-ans - -Make things as simple as...

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P2 Week 1 Significant figures, Word problems 1 -Make things as simple as possible, but no simpler -A. Einstein

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In high school, I have had (A) No Physics, no calculus (B) No Physics, calculus (C) Physics, calculus (D) Physics, AP calculus (E) AP Physics, AP calculus 2
Signifcant fgures £ Significant figures keep track of how precise a measured (or estimated) quantity is £ How many significant figures does 0.0012 have? ¤ Answer is 2. £ Don’t count the zeros before the first non-zero digit. £ Count all other digits. £ How many significant figures does 0.00102 have? ¤ A : 1 ¤ B : 6 ¤ C : 7 ¤ D : 2 ¤ E : 3 3

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Signifcant fgures £ Is 0.00120 different from 0.0012 in any way? ¤ YES! ¤ By writing 0.00120 you are asserting that the digit after 2 is zero . So 0.00120 is accurate to one more decimal point than 0.0012 ¤ Number of significant figures in 0.00120 is 3 while the number of significant figures in 0.0012 is 2. £ But what do you do if there is no decimal point? ¤ Example, how many significant figures does 10 have? Or 11? ¤ A way to avoid this confusion is to use scientific notation . 4
Scientifc notation £ Scientific notation is written in base 10. It has a coefficient and an exponent . ¤ 0.0012 is written as 1.2 x 10 -3 when SCIENTIFIC notation is adopted. 1.2 is the coefficient . -3 is the exponent. Rules: ¥ One digit before decimal point. ¥ The digit before decimal point cannot be 0 ± In other words, coefficient must be greater than or equal to 1 and less than 10. ¥ As many digits after decimal point as required. ¤ The number of significant figures is the total number of digits (including zeros) in the coefficient . 5

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Scientifc notation problem £ How would you express 0.0234 in scientific notation correctly? ¤ A : 0.234 × 10 -1 ¤ B : 0.0234 × 10 0 ¤ C : 2.34 × 10 -2 ¤ D : 2.34 × 10 -1 ¤ E : 23.4 × 10 -3 6
Scientifc notation problem £ How would you express 0.0234 in scientific notation correctly? ¤ C : 2.34 × 10 -2 7

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Signifcant fgures and Formulae £ In the formula v=u+a t^2 / 2, you should take the 2 as known to infinite precision -- it plays no role in setting the significant figures of your answer. 8
Signifcant fgures and addition £ Practical Rule for addition and subtraction : Supply answer to the smallest number of decimal places from among the numbers involved in the calculation, rounding up if necessary. £ Example 1: 0.0012 + 0.0992 = 0.1004 £ Example 3: 0.012 - 0.0998 = - 0.088 Keep answer to 3 decimal places £ Example 2: 0.00120 + 0.0992 = 0.1004 Keep answer to 4 decimal places. Keep the answer as is (all numbers known to 4 decimal places). 9

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Sig Fig problem 1 £ You add 1.234 to 0.01 in your exam. The calculator will give 1.244. You should express the answer as ¤ A : 1.244 ¤ B : 1.24 ¤ C : 1.25 ¤ D : 1.2 ¤ E : 1 10
Sig Fig problem 2 £ You add 1.235 to 0.01 in you exam. The calculator will give 1.245. You should express the answer as ¤ A : 1.245 ¤ B : 1.24 ¤ C : 1.25 ¤ D : 1.2 ¤ E : 1 11

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## This note was uploaded on 12/12/2011 for the course PHYS 2 taught by Professor Staff during the Fall '08 term at UC Irvine.

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P2F11-Week1-Barwick-ans - -Make things as simple as...

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