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Chapter 01

# Chapter 01 - 5 1.1 1 mi 5280 ft mi 12 in ft 2 54 cm in 1 km...

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1.1: ( 29 ( 29 ( 29 ( 29 km 61 . 1 cm 10 km 1 . in cm 54 . 2 ft in. 12 mi ft 5280 mi 1 5 = × × × × Although rounded to three figures, this conversion is exact because the given conversion from inches to centimeters defines the inch. 1.2: . in 9 . 28 cm 54 . 2 in 1 L 1 cm 1000 L 473 . 0 3 3 3 = × × 1.3: The time required for light to travel any distance in a vacuum is the distance divided by the speed of light; ns. 10 3.33 s 10 33 . 3 s m 10 3.00 m 10 3 6 8 3 × = × = × - 1.4: . m kg 10 13 . 1 m 1 cm 100 g 1000 kg 1 cm g 3 . 11 3 4 3 3 × = × × 1.5: ( 29 ( 29 ( 29 L. 36 . 5 cm 1000 L 1 in cm 54 . 2 in 327 3 3 3 = × × 1.6: . . oz 16 bottle 1 gal 1 . oz 128 L 788 . 3 gal 1 m 1 L 1000 m 1 3 3 × × × × bottles 2112 bottles 9 . 2111 = The daily consumption must then be . da bottles 78 . 5 da 24 . 365 yr 1 yr bottles 10 11 . 2 3 = × × 1.7: ( 29 ( 29 . hr km 2330 mi km 61 . 1 hr mi 1450 = × ( 29 ( 29 s. m 648 s 3600 hr 1 km m 10 hr km 2330 3 = × × 1.8: . h mi 67 h 24 day 1 day 14 fortnight 1 furlongs 8 mile 1 fortnight furlongs 000 , 180 = × × × 1.9: . gal mi 3 . 35 gal 1 L 788 . 3 km 1.609 mi 1 L km 0 . 15 = × ×

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1.10: a) s ft 88 mi 1 ft 5280 s 3600 h 1 hr mi 60 = b) 2 2 s m 8 . 9 cm 100 m 1 ft 1 cm 48 . 30 s ft 32 = c) 3 3 3 3 m kg 10 g 1000 kg 1 m 1 cm 100 cm g 1.0 = 1.11: The density is mass per unit volume, so the volume is mass divided by density. ( 29 ( 29 3 3 3 cm 3077 cm g 5 . 19 g 10 60 = × = V Use the formula for the volume of a sphere, , 3 4 3 r V π = to calculate ( 29 cm 0 . 9 4 3 : 3 / 1 = = π V r r 1.12: % 58 . 0 100 ) s 10 (3.16 s) 10 π s 10 16 . 3 ( 7 7 7 = × × × - × 1.13: a) %. 10 1 . 1 m 10 890 m 10 3 3 - × = × b) Since the distance was given as 890 km, the total distance should be 890,000 meters. To report the total distance as 890,010 meters, the distance should be given as 890.01 km. 1.14: a) ( 29 ( 29 2 mm 72 mm 98 . 5 mm 12 = × (two significant figures). b) mm 12 mm 98 . 5 = 0.50 (also two significant figures). c) 36 mm (to the nearest millimeter). d) 6 mm. e) 2.0.
1.15: a) If a meter stick can measure to the nearest millimeter, the error will be about %. 13 . 0 b) If the chemical balance can measure to the nearest milligram, the error will be about %. 10 3 . 8 3 - × c) If a handheld stopwatch (as opposed to electric timing devices) can measure to the nearest tenth of a second, the error will be about %. 10 8 . 2 2 - × 1.16: The area is 9.69 ± 0.07 cm 2 , where the extreme values in the piece’s length and width are used to find the uncertainty in the area. The fractional uncertainty in the area is 2 2 cm 69 . 9 cm 07 . 0 = 0.72%, and the fractional uncertainties in the length and width are cm 5.10 cm 01 . 0

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