Simple Nature - Light and Matter

force, and the best unit to use for mass is the slug, which is about14.6 kg.)More important than memorizing conversion factors is understandingthe right method for doing conversions. Even within theSI, you may need to convert, say, from grams to kilograms. Differentpeople have different ways of thinking about conversions, butthe method I’ll describe here is systematic and easy to understand.The idea is that if 1 kg and 1000 g represent the same mass, thenwe can consider a fraction like10 3 g1 kgto be a way of expressing the number one. This may bother you. Forinstance, if you type 1000/1 into your calculator, you will get 1000,not one. Again, different people have different ways of thinkingabout it, but the justification is that it helps us to do conversions,and it works! Now if we want to convert 0.7 kg to units of grams,we can multiply kg by the number one:0.7 kg × 103 g1 kgIf you’re willing to treat symbols such as “kg” as if they were variablesas used in algebra (which they’re really not), you can thencancel the kg on top with the kg on the bottom, resulting in0.7 kg × 103 g1 kg = 700 g .To convert grams to kilograms, you would simply flip the fractionupside down.One advantage of this method is that it can easily be applied toa series of conversions. For instance, to convert one year to units ofseconds,1 ✘year ✘ × 365 ✟days✟ 1 ✘year✘ × 24 ✘ hours ✘✘1 ✟ day ✟× 60 ✟ min ✟1 ✘hour ✘✘ × 60 s1 ✟ min ✟ == 3.15 × 10 7 s .Should that exponent be positive, or negative?A common mistake is to write the conversion fraction incorrectly.For instance the fraction10 3 kg1 g(incorrect)does not equal one, because 10 3 kg is the mass of a car, and 1 g isthe mass of a raisin. One correct way of setting up the conversion30 Chapter 0 Introduction and Review