Everyday Math Demystified, 2nd edition Stan Gibilisco Explanations for Quiz Answers in Chapter 10 1. According to the chapter text, if we increase the current through a component whose resistance doesn't change, then the voltage across that component increases in proportion. For example, if we double the current, then we double the voltage. We can reverse this logic and say that if we reduce the current through a component whose resistance never changes, then the voltage across that component will decrease. The correct choice is C. 2. Power represents the rate at which energy is produced or consumed, or otherwise manifests itself in the "real world." One watt of power, in effect, equals one joule of energy produced or consumed per second. The answer is B. 3. As we learned in Chapter 9, the prefix multiplier nano- (abbreviated n) translates to "10-9 of." Therefore, a nanogram (1 ng) equals 10-9 g. The correct choice is A. 4. The prefix multiplier micro- (abbreviated µ) translates to "10-6 of." Therefore, a microgram (1 µg) equals 10-6 g, which in turn equals 1000 ng, because 10-6 is 1000 times as great as 10-9. The correct choice is B. 5. The mass of an object stays the same, no matter where we take it: the earth, Mars, the moon, Pluto, an asteroid, or even interstellar space. If we take a rock from the earth to Mars, its mass won't change at all. The correct choice is A. 6. An object's weight depends on the strength of gravity as well as its mass. If we have a rock whose mass stays constant and take it from the earth to Mars, where the gravitational field is only 37 percent as strong, we'll find that the rock weighs only 37 percent of its weight on earth. (In this case, the 4.4-pound rock would only weigh 4.4 x 0.37 = 1.6 pounds on Mars.) The answer is D. 7. Kelvin figures never go below zero. If somebody tells you that a sample of water has a temperature of -15 K, you can be sure that he's misinformed. The answer is D. 8. Steradians quantify three-dimensional (3D) angles, also called solid angles. In two dimensions (2D), such as going halfway around a circle, we would specify angles in radians. Steradians don't mean anything in a 2D scenario. The correct choice is D. 9. We need Table 10-1 to work out this problem. It tells us that a nautical mile (1 nmi) equals 1852 m. From that information, we can deduce that 1 nmi equals 1.852 km, because 1 km = 1000 m. When we reverse the relation, we see that 1 km equals approximately 1 / 1.852 = 0.5400 nmi. The correct choice is C. 10. On earth, a pound (1 lb) represents approximately 0.4535 kilograms (kg) according to Table 10-1. If we want to change that value to micrograms (µg), we must multiply by 109, getting 0.4535 x 109 µg. That expression isn't in proper scientific notation, though. We must multiply the coefficient by 10 (move the decimal point one place to the right) and then reduce the power of 10 by 1, getting 4.535 x 108 µg. The answer is C.