Measurement (Ch 3) Handout #2 answers Q # 1 #sig figs A 6.7501 5 F. 2500. 4 B 0.157 3 g. 2500 2 C 28 2 h. 2.500 4 d. 28. 2 i. 0.070 2 e. 28.0 3

Q #1 30.07 4 S. 437. 3 0.1060 4 T. 100 1 0.0067 2 U. 0.000437 3 0.00230 3 V. 0.0901 3 20.509 5 W. 0.05030 4 54 020. 5 X. 12 010 4 54 020 4 Y. 1 000 1 2.690 4 Z. 1 000. 4 437 3 aa. 10 1

Keeping sig figs when converting to sci not. 2A. 55 000. 5 5.5000 x 10 4 55 000 2 5.5 x 10 4 0.0001 1 1 x 10 – 4 0.00010 2 1.0 x 10 – 4 0.0500 3 5.00 x 10 – 2 0.05 1 5 x 10 – 2

Keeping sig figs when converting to sci not. 2G. 0.9990 4 9.990 x 10 – 1 0.999 3 9.99 x 10 – 1 5 902 000. 7 5.902 000 x 10 6 J. 5 902 000 4 5.902 x 10 6

3. Keeping sig figs when converting from sci not into standard form. A. 3.0 x 10 – 5 2 0. 000 030 2 B. 3 x 10 – 5 1 0. 000 03 1 3.00 x 10 – 5 3 0. 000 0300 3 All ok so far.

D. 8.0 x 10 3 2 8 000 = 1 and 8 000. = 4 NOT POSSIBLE to convert “D” into standard! E. 8.000 x 10 3 4 8 000. = 4 F. 8.00 x 10 3 3 8 000 = 1 NOT POSSIBLE to convert “F” into standard!

G. 9.360 x 10 3 4 9 360. = 4 H. 9.3600 x 10 3 5 9 360.0 = 5 I. 9.36 x 10 3 3 9 360 = 3

J. 1.220 x 10 4 4 12 200. = 5 and 12 200 = 3 NOT POSSIBLE to convert “J” into standard! K. 1.2200 x 10 4 5 12 200. = 5 L. 1.22000 x 10 4 6 12 200.0 = 6

A. 7.6 x 10 22 (a very large number) B. 4150 = 4.15 x 10 3 4. Scientific Notation is used with measurements for 2 main reasons: working with very large or very small numbers; and, it allows you to be very clear about which zeros are merely place-holding, and which are significant. A. 7.6 x 10 22 (a very large number) B. 4150 = 4.15 x 10 3 3 x 10 –2 5 (a very small number) 5.290 x 10 – 3 E. 5.29 x 10 – 3

5. Take the following out of scientific notation: 3 x 10 2 = 300 # sig figs = 1 2.00 x 10 -3 = 0.00200 # sig figs = 3

6. Sig Figs in Measurements: Review. B. 200 = 1 C. 804.580 = 6 D. 0.000 480 = 3 E. 3000. = 4 F. 250.00 = 5 G. 78 300 = 3 H. 0.011 = 2

Sig Figs in Counts and/or “Unit Conversions” that are established by definition: A through I: all are “unlimited” (infinite).

8. Key concept: “In general, a calculated answer can not be more precise than the least precise measurement from which it was calculated.” And, as long as the measurements are in the same unit, then the “least precise” will be those that contain the fewest decimal places to the right of the decimal point. Please see p 67: 0.6 m is less precise than 0.61 m, which is less precise than 0.607 m

p. 68 (rounding)— “Once you know the number of significant figures your answer should have, round to that many digits, counting from the left. If the digit immediately to the right of the last significant digit is less than 5, it is simply dropped and the value of the last significant digit stays the same. If the digit in question is 5 or greater, the value of the digit in the last significant place is increased by 1.”

Before proceeding, lets go back to page 67 (the 3 rulers). Rounding is at least a 2 step (not a 1 step) mental process; and, deciding what sig fig to round to should always be the first step. Rounding Example: 0.6 m + 0.61 m + 0.607m = ? calculator answer: _____________ Remember: “a calculated answer cannot be more precise than the least precise measurement from which it was calculated.” After you round=, what is your final answer? _____ Choices: 1.817 1.82 1.8 2

Round to 1 sig fig: [start counting sig figs from the left] 0.072  0.07 0.0750  0.08 0.0975  0.1 Check: each answer has 1 sig fig.

Round to 2 sig fig: 44.511  45 445  450 444  440 Check: each answer has 2 sig fig.

Round to 3 sig fig: 5.603  5.60 5.606  5.61 560.3  560. Check: each answer has 3 sig fig.

Round to 3 sig fig: 689.75  690. 0.06897504  0.0690 68.97 69.0 Check: each answer has 3 sig fig.

Round to 4 sig fig: 1.1595  1.160 11,595  11,600 = 3 sig figs NOT CORRECT 11,600. = 5 sig figs NOT CORRECT 1.160 x 10 4 = only way to express this in 4 sig figs 999,904  999,900 Check: each answer has 4 sig fig.

Round to 1 sig fig: 8.50  9 9.60  10 11  10 Round to 2 sig figs: 0.00775  0.0078 0.0796  0.080 796  800 = 1 sig fig NOT CORRECT  800. = 3 sig figs NOT CORRECT  8.0 x 10 2 is the only way to round to 2 sig figs!

Addition and Subtraction, p 70: Book: The answer to an addition or subtraction calculation should be rounded to the same number of decimal places as the measurement with the least number of decimal places. My summarization: When adding and subtracting a set of measurements, I round to the right-most common sig fig. 12.5 2 349.0 8.2 4 369.7 6 “Round up” = 369.8

meters meters “Round down” p. 70 # 5 #6 14.2 8.7 3 A 61.2 0.9 12 9.3 5 23.842 = 23.8 8.6 “round down” 79.1 5 “Round up” = 79.2 meters B 9.44 C 1.36 D. 34.61 -2.11 10.17 -17.3 7.33 11.53 17.3 1 = 17.3 meters meters “Round down”

p. 71 Multiplication / division: “You need to round the answer to the same number of sig figs as the measurement with the least number of sig figs”. 7.A. 8.3 x 2.22 = 18.426  18 (2 sig figs) because 8.3 has only 2 sig figs.

p. 71 Multiplication / division: “You need to round the answer to the same number of sig figs as the measurement with the least number of sig figs”. 7B. 8432 / 12.5 = 674.56  675 (3 sig figs) Because 12.5 has only 3 sig figs.

p. 71 Multiplication / division: “You need to round the answer to the same number of sig figs as the measurement with the least number of sig figs”. 7C. 35.2 x (1min/60 sec) = 0.5866 6 0.587 3 sig figs because (1min/60s) has unlimited sig figs, and 35.2 has 3 sig figs. And, 3 is < unlimited!

8. 22. 4 meters x 11. 3 meters x 5. 2 meters = 1316 8. 22.4 meters x 11.3 meters x 5.2 meters = 1316.224 m3  1300 m3 (2 sig figs) Because 5.2 has 2 sig figs Next class there will be a QUIZ on all 3 measurement handouts, covering text pp 63 – 71.