Strategy: Multiply the given number by conversion factors to obtain the desired units m

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1 Homework 1 Solutions 2. Picture the Problem: This is simply a units conversion problem. Strategy: Multiply the given number by conversion factors to obtain the desired units. Solution: (a) Convert the units: m 5 70 m m m (b) Convert the units again: m 1 km 8 70 m km m 1000 m Insight: The inside back cover of the textbook has a helpful chart of the metric prefixes. 14. Picture the Problem: This is a significant figures question. Strategy: Follow the given rules regarding the calculation and display of significant figures. Solution: Round to the 3 rd digit: m/s m/s Insight: It is important not to round numbers off too early when solving a problem because excessive rounding can cause your answer to significantly differ from the true answer. 15. Picture the Problem: The parking lot is a rectangle m Strategy: The perimeter of the parking lot is the sum of the lengths of its four sides. Apply the rule for addition of numbers: the number of decimal places after addition equals the smallest number of decimal places in any of the individual terms m m m Solution: 1. Add the numbers: 2. Round to the smallest number of decimal places in any of the individual terms: m = m m m Insight: Even if you changed the problem to m m you d still have to report m as the answer; the 2 is considered an exact number so it s the m that limits the number of significant digits. 16. Picture the Problem: The weights of the fish are added. Strategy: Apply the rule for addition of numbers, which states that the number of decimal places after addition equals the smallest number of decimal places in any of the individual terms. Solution: 1. Add the numbers: lb = lb

2 2. Round to the smallest number of decimal places in any of the individual terms: lb 26.6 lb Insight: The 12.1 lb rock cod is the limiting figure in this case; it is only measured to within an accuracy of 0.1 lb. 17. Picture the Problem: This is a significant figures question. Strategy: Follow the given rules regarding the calculation and display of significant figures. Solution: 1. (a) The leading zeros are not significant: has 2 significant figures 2. (b) The middle zeros are significant: has 4 significant figures Insight: Zeros are the hardest part of determining significant figures. Scientific notation can remove the ambiguity of whether a zero is significant because any trailing zero to the right of the decimal point is significant. 20. Picture the Problem: This is a units conversion problem. Solution: 1. (a) Find the length in feet: 2. Find the width in feet: 3.28 ft 631 m 2069 ft 1 m 3 ft 707 yd 2121 ft 1 yd 3. Find the volume in cubic feet: 8 V LWH 2069 ft 2121 ft 110 ft (b) Convert to cubic meters: m ft m 3.28 ft 21. Picture the Problem: This is a units conversion problem. Solution: 1. Find the length in feet: 2. Find the width and height in feet: 17.7 in 1 ft 2.5 cubit 3.68 ft 1 cubit 12 in 17.7 in 1 ft 1.5 cubit 2.21 ft 1 cubit 12 in V LWH 3.68 ft 2.21 ft 2.21 ft 18 ft 3. Find the volume in cubic feet: 3

3 equal something other than one. They are often helpful in displaying a number in a convenient,

4 22. Picture the Problem: This is a units conversion problem. Strategy: Convert the frequency of cesium-133 given on page 4 to units of microseconds per megacycle, then multiply by the number of megacycles to find the elapsed time. Solution: Convert to micro seconds per megacycle and multiply by 1.5 megacycles: 6 1 s 1 10 cycles 1 s ,192, 631, 770 cycles Mcycle 1 10 s s Mcycle 160 s 1.6 Mcycle Insight: Only two significant figures remain in the answer because of the 1.5 Mcycle figure given in the problem statement. The metric prefix conversions are considered exact and have an unlimited number of significant figures, but most other conversion factors have a limited number of significant figures. 23. Picture the Problem: This is a units conversion problem. Solution: Convert feet to kilometers: 1 mi km 3212 ft km 5280 ft 1 mi 26. Picture the Problem: This is a units conversion problem. Solution: Convert carats to pounds: 0.20 g 1 kg 2.21 lb ct 0.23 lb ct 1000 g kg

5 27. Picture the Problem: This is a units conversion problem. Solution: 1. (a) The speed must be greater than 55 km/h because 1 mi/h = km/h. 2. (b) Convert the miles to kilometers: mi km km h mi h 28. Picture the Problem: This is a units conversion problem. Solution: Convert m/s to miles per hour: 8 m 1 mi 3600 s 8 mi s 1609 m 1 h h 29. Picture the Problem: This is a units conversion problem. Solution: Convert to ft per second per second: m 3.28 ft ft s 1 m s 30. Picture the Problem: This is a units conversion problem. In this problem, one jiffy corresponds to the time in seconds that it takes light to travel one centimeter. Solution: 1. (a): Determine the magnitude of a jiffy: 1 s 1 m s m 100 cm cm jiffy s

6 60 s 1 jiffy 1 minute min s 2. (b) Convert minutes to jiffys: Picture the Problem: The volume of the oil is spread out into a slick that is one molecule thick. Strategy: The volume of the slick equals its area times its thickness. area. Use this fact to find the Solution: Calculate the area for the known volume and thickness: 3 V 1.0 m 1 m A h 0.50 m 1 10 m Insight: Two million square meters is about 772 square miles! 33. Picture the Problem: This is a units conversion problem. Then use a ratio to find the factor change in part (b). Solution: 1. (a) Convert square inches to square meters: 2 1 m A 8.5 in 11 in in (b) Calculate a ratio to find the new area: Anew LnewW 2L new old 2Wold A L W L W A old old old old old Insight: If you learn to use ratios you can often make calculations like these very easily. new 1 4 A old 1 4 Always put the new quantity in the numerator and the old quantity in the denominator to make the new quantity easier to calculate at the end. 34. Picture the Problem: This is a units conversion problem. Solution: 1. Convert m/s to ft/s: 2. (b) Convert m/s to mi/h: m 3.28 ft ft/s s m m 1 mi 3600 s s 1609 m 1 h

7 35. Picture the Problem: This is a units conversion problem. Solution: Convert meters to feet: m 3.28 ft ft/s 2 s 1 m 2

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