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1.1 Introduction - units and calculations Due: 11:59pm on Sunday, September 17, 2023 You will receive no credit for items you complete after the assignment is due. Grading Policy Significant Figures in Calculations Learning Goal: To learn how to round an answer to the correct number of significant figures. When we report a measurement in science, we are careful to report only digits known with certainty, plus a final digit that is recognized to be uncertain. We call this set of digits significant figures . Often, these numbers are used in calculations. When we use a calculator, the calculator does not automatically account for significant figures, so we have to do so ourselves. There are some basic rules for handling significant figures in calculations as shown in the table and outlined to the right. Significant Figure in Calculations MULTIPLICATION DIVISION 123.1 23 = 2.8 10 3 123.1 / 23 = 5.4 4 s.f. 2 s.f. 2 s.f. 4 s.f. 2 s.f. 2 s.f. ADDITION SUBSTRACTION 123. 1 + 23 = 146 123. 1 - 23 = 1.00 10 1 (also 100.) 1 d.p 0 d.p. 0 d.p. 1 d.p. 0 d.p. 0 d.p. note : s.f. stands for "significant figures" d.p. stands for "digits to the right of the decimal point" Multiplication and division When multiplying or dividing, the final answer is rounded to the same number of significant figures as the measured number with the fewest significant figures. Addition and subtraction When adding or subtracting, the final answer is rounded to the same number of digits to the right of the decimal point as the measured number with the fewest digits to the right of the decimal point. This item does not cover measured values without a decimal point, which may involve interpreting values with an ambiguous number of significant figures. Part A Compute . Round the answer appropriately. × × × . 3.5 × 4.48697

Express your answer numerically using the proper number of significant figures. Hint 1. How to approach the problem For multiplication or division, the final answer should be rounded to the same number of significant figures as the given value with the fewest significant figures. Hint 2. Determine the number of significant figures in the final answer How many significant figures should be shown in the final answer after rounding? Express the number of significant figures as an integer. ANSWER: ANSWER: Correct Because this calculation involved multiplication, the final answer must be rounded to the same number of significant figures as the measured value with the fewest significant figures. Part B Compute . Round the answer appropriately. Express your answer numerically using the proper number of significant figures. Hint 1. How to approach the problem For multiplication or division, the final answer should be rounded to the same number of significant figures as the given value with the fewest significant figures. Hint 2. Determine the number of significant figures in the final answer How many significant figures should be shown in the final answer after rounding? Express the number of significant figures as an integer. 2 16 3.5 × 4.48697 = 1240.64/12.5

ANSWER: ANSWER: Correct Because this calculation involved division, the final answer must be rounded to the same number of significant figures as the measured value with the fewest significant figures. Part C Compute . Round the answer appropriately. Express your answer numerically using the proper number of significant figures. Hint 1. How to approach the problem The rules for addition and subtraction differ from those for multiplication and division. For addition and subtraction, the answer should be rounded to the same number of decimal places as the number having the fewest decimal places. Hint 2. Determine the number of digits How many digits to the right of the decimal point should the final answer have after rounding? Express the number of significant figures as an integer. ANSWER: ANSWER: 3 99.3 = 1240.64 12.5 9.3456 + 2140.56 2 2149.91 9.3456 + 2140.56 =

Correct Because this calculation involved addition, the final answer must be rounded to the same number of digits to the right of the decimal point as the measured value with the fewest number of digits to the right of the decimal point. Part D Compute . Round the answer appropriately. Express your answer as an integer using the proper number of significant figures (e.g. 12300 ). Hint 1. How to approach the problem The rules for addition and subtraction differ from those for multiplication and division. For addition and subtraction, the answer should be rounded to the same number of digits as the value with the last significant digit in the highest place value. For example, the value 12345 has a 1 in the ten thousands place, a 2 in the thousands place, a 3 in the hundreds place, a 4 in the tens place, and a 5 in the ones place. In this specific value, there are no trailing zeros. The last significant digit is the 5 in the ones place. Hint 2. Determine the number of digits Determine the position of the last significant digit in and . Drag the appropriate numbers to their respective bins. ANSWER: 4.659 × − 2.14 × 10 4 10 4 4.659 × 10 4 2.14 × 10 4

Hint 3. Determine the number of significant figures in the final answer has the final significant digit in the tens place and . has the final significant digit in the hundreds place. To what place will the final answer be rounded? ANSWER: Reset Help 4.659 × 10 4 2.14 × 10 4 4.659 × 10 4 2.14 × 10 4

ANSWER: Correct Because this calculation involved subtraction and both values have no digits following the decimal point, the final answer must be rounded to the same number of digits as the measured value with the fewest number of significant digits to the left of the decimal point. Rounding It will be helpful to remember two guidelines about significant figures. 1. After multiplication or division, the answer cannot have more significant figures than any of the original numbers. 2. After addition or subtraction, the answer cannot have more digits to the right of the decimal point than any of the original numbers. After determining the appropriate number of significant figures, round off your final answer. 1. If the first digit you drop is greater than or equal to 5, add 1 to the last digit you keep. You are rounding up. 2. If the first digit you drop is less than 5, do nothing to the digits you keep. You are rounding down. Part A A bakery measured the mass of a whole cake as 0.840 . A customer bought one slice of the cake and measured the mass of the slice as 0.1171 . What is the mass of the remaining cake, without the one slice? Express your answer in kilograms using the appropriate number of significant figures. ones tens hundreds thousands ten thousands 2.52x10^4 4.659 × − 2.14 × = 10 4 10 4 kg kg

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