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3.4 Dividing and Multiplying Measured Numbers

3.4 Dividing and Multiplying Measured Numbers. How Accurate are your calculations? a pebble: mass = 12.36 g volume = 4.7 cm 3 12.36 g = 2.62978723 g/cm 3 4.7 cm 3

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3.4 Dividing and Multiplying Measured Numbers

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  1. 3.4 Dividing and Multiplying Measured Numbers How Accurate are your calculations? a pebble: mass = 12.36 g volume = 4.7 cm3 12.36 g = 2.62978723 g/cm3 4.7 cm3 RULE: Your answer should have as many digits as the measured number with the fewest digits. (but calculate 1 digit more to round up or down) mass = 12.36 g volume = 4.7 cm3 4.7 is only two digits, so my answer is 12.36 = 2.6 g/cm3 4.7 The 2 and the 6 are significant digits-others dropped

  2. An example of block of wood: 4.82 cm 11.05 cm X 1.28 cm 68.174080 cm3 • Correct answer: 68.2 cm3 • If last digit 0 it is significant (remember 1.3 reading scales) • But zeros in front are not counted. For example: • 0.86 Both of these numbers have 2 significant numbers. • 0.045 • In this case the zeros are not counted.

  3. 7. How many significant digits are in each of the following measurements? a. 4.0 cm3 Answer: 2 b. 78.21 g Answer: 4 c. 7.05 cm Answer: 3 d. 5.40 g Answer: 3 e. 0.033 m Answer: 2 f. 225 cm Answer : 3 g. 0.01 g Answer: 1 h. 0.930 m Answer: 3

  4. 8. Do the following calculations to the proper number of digits. a. 125/23.7 Answer: 5.27 b. 20.5/51.0 Answer: .402 c. 0.065/32.5 Answer: .0020 d. 1.23/0.72 Answer: 1.7 e. 4.72 X 0.52 Answer: 2.5 f. 6.3 X 10.08 Answer: 64 g. 1.55 X 2.61 X 5.3 Answer: 21 h. 3.01 X 5.00 X 25.62 Answer: 386

  5. 9. Suppose the measured dimensions of a rectangle are 3.62 cm and 12.06 cm. a. With a calculator, determine the area of the rectangle and report all the digits on the display. Answer:43.6572 b. Suppose each measurement could be off by ± 0.02 cm. Report the least and greatest possible values for the area of the rectangle. Use calculator and report all the digits. Answer: For + 0.02 3.62 would be 3.64 12.06 would be 12.08 so 3.64 X 12.08 =43.9712 Answer: For -0.02 3.62 would be 3.60 12.06 would be 12.04 so 3.60 X 12.04 = 43.344 c. Which of the digits calculated in part (a) are the same as those calculated in part (b)? Answer: 43 (the first 2 digits are the same).

  6. Why should you report your answer to part (a) using only 3 digits, as suggested by the rule of thumb on page 45? Original answer: 43.6572 Answer if each measurement off by +0.02: 43.9712 Answer is each measurement off by -0.02: 43.344 UNCERTAINTY LIES IN THE THIRD DIGIT , BUT NOTHING IS KNOWN ABOUT THE FOURTH.

  7. 10. Suppose that a pebble has a mass at 12.36 g and a volume of 4.7 cm3 With a calculator, determine the density of the pebble and report all the digits on the display. Answer: 2.629787234 g/cm3 b. Suppose the measurements could be off by ± 0.01 g and ± 0.01 cm3. Answer: Least possible value: 12.35/4.8 = 2.572916667 g/cm3 Greatest possible value: 12.37/4.6 = 2.689130435 g/cm3 c. Which of the digits calculated in part b are the same as those calculated in part (a)? Answer: Only the 1st digit is the same d. Why should you report your answer to part (a) using only two digits? Answer: The uncertainty lies in the second digit, nothing is know about the third digit.

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