Exercise Questions: 4

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Exercise Questions: 4. What is the difference between reporting the quantity nine inches as 9 inches and 9.00 inches? When the measurement is expressed in 9 inches, it may be rounded from any number between 8.5 and 9.4. However, when the measurement is expressed in 9.00 inches, it indicates that 9 is a number accurate to two decimal places, rather than rounded. Even so, we can't tell if 9 inches is a integer, because 9.003 isn't ruled out.

13. What is density? Give two examples of possible units for density. Density is the ratio of an object's mass to its volume. Gram and kilogram.

Problems: 15. Express each of the following in scientific notation: a. 0.000851 g 8.51 x 10-4

b. 38,041,430 (population of California) 3.8 x 107

c. 299,790,000 m/s (speed of light) 3.0 x 108

d. 313,914,040 (U.S. population) 3.1 x 108

17. Express each of the following in decimal notation: a. 149 x 106 km (average distance between Earth and the Sun) 149,000,000 km b. 7.9 x 10-11 m (radius of a hydrogen atom) 0.000000000079 m c. 4.54 x 109 yr (age of Earth) 4,540,000,000 yr d. 6.4 x 106 m (radius of Earth) 6,400,000 m

19. The circumference of Earth at the equator is 40,075 km. Convert this distance into each of the following units: a. meters 40,075,000 m b. miles 24,901.5 miles c. feet 131,479,658.8 feet

23. A car has a fuel efficiency of 27 miles per gallon. What is its efficiency in kilometers per gallon? 43.4 km/gallon

25. Perform each of the following conversions within the metric system: a. 4332 mm to m 4.332 m b. 1.76 kg to g 1,760 g c. 4619 mg to kg 0.004619 kg d. 0.0117 L to mL 11.7 ml

37. The following graph shows the concentration of an atmospheric pollutant, carbon monoxide, for the period 1990–2015. As shown by this graph, carbon monoxide levels have decreased in the atmosphere because of mandatory reductions legislated by the Clean Air Act. a. What is the total decrease in carbon monoxide over this period? 6.1 - 1.5 = 4.6 ppm b. What is the average yearly decrease in carbon monoxide over this period? 4.6 / 25 = 0.184 ppm/yr

 

 

c. What is the total percentage decrease in carbon monoxide over this period? 4.6 / 6.1 x 100% = 75% d. What is the average yearly percentage decrease in carbon monoxide over this period? 75% / 25 = 3% /yr

45. A metal cylinder has a radius of 0.55 cm and a length of 2.85 cm. Its mass is 24.3 grams. a. What is the density of the metal? For a cylinder, V = π r 2 x h, where r is the radius of the cylinder and h is the height of the cylinder. π = 3.14. 24.3 / (0.95 x 2.85) = 9 grams b. Compare the density of the metal to the densities of various substances listed in Table 2.4. Can you identify the metal? Copper

Feature Problems and Projects: 52. Consider each of the following balances. Which one is the most precise? C. 5.4249 g Which one is the least? A. 5.42 g How much uncertainty is associated with each balance? (5.42 + 5.424 + 5.4249) / 3 = 5.4229 g

A. 5.4229 - 5.42 = +0.0029 g B. 5.4229 - 5.424 = +0.0011 g C. 5.4229 - 5.4249 = +0.002 g

53. Each of the following coins is photographed to scale. Measure each using a metric ruler (in cm) and record the diameter to the precision reflected in the ruler. Make a simple graph of the value of the coin (x-axis) and the diameter of the coin (y-axis). Is there any correlation between these two quantities? Which coin does not fit the general trend?

1. cent: 1.8 cm 2. 5-cents: 2cm 3. dime: 1.8 cm 4. quarter : 2.3 cm 5. half: 3cm 6. one: 3.8 cm

There is a correlation between these two quantities. As the value of a coin increases, so does its diameter, except for the dime.

 

 

Example A1.1 Determining the Number of Significant Figures How many significant figures are in each of the following numbers? 0.0087 two 4.50 x 105 three 45.5 three 164.09 five 0.98850 five

Example A1.3 Carry out the following calculation to the correct number of significant digits: 4.342 + 2.8703 + 7.88 - 2.5 = 12.6