I’ll try to use more realistic (i.e., harder) But I deliberately chose a simple example You might be asking yourself, “ Why all the fuss?Īnybody knows that to convert hours to minutes you have to multiply byĦ0.” Well, yes, that’s true. Multiplying is the same as the value before multiplying-butĮxpressed in different units, which of course is the whole point. Of the fraction are equal, the fraction equals 1 and the value after Is the same as 327 cents, when you multiply by the “carefully chosenįorm of 1”, 100 cents/dollar or 100 cents/euro. Think of it this way: 3.27 dollars or euros Without units or with different units, just as 8 x is differentįrom both 8 and 8 y. You bake a turkey for 270 minutes or 4½ hours, either way youĪ number with units is different from a number You should be able to convince yourself that if The answer is that we didn’t start with a “dimensionless” pure numberĤ.5, but with 4.5 hours and we didn’t end up with a pure number 270īut with 270 minutes. Summary: to convert units, construct a fraction that isĮqual to 1, multiply the original measurement by that fraction, and Just as you would divide through by x when x was in both top and bottom, so you can divide through by the “variable” hr: Notice that you have hours (hr) in both top and bottom. Now, x times y/ z is the same as xy/ z, so our units expression is the same as To do the conversion, simply multiply by that well-chosen form of 1: (I’ll explain a little later why I divided through by 1 hr and not 60 min.) So go back to the 4½ hours that we wanted to convert to minutes. Why did I do that? Because if (60 min)/(1 hr) = 1, then I can multiply any measurement by that fraction and not change its value. If you had 60 x = 1 y, you could certainly divide both sides by 1 y.) After dividing, you have (Remember you can do this because you treat the unit “hour” just like a variable. Suppose you want to convert four and a half hours to minutes. Your head, so that I can show the steps excruciatingly clearly. Obvious, right? “So why mention it?” I hear you ask.īecause multiplying by 1-a carefully chosen form ofĭeliberately pick an easy one, one you could probably do in You can multiply anything by 1 and not change its To convert units, there’s only one other thing you need to bear in And when you divideģ2 miles by 4 hours to get 8 miles/hour, that’s exactly You can’t add 32 ft to 32 ft/sec, any more than youĬan add 32 x to 32 x/ y. Once you grasp this, you see at once why the laws of units work as The method for converting units comes right fromģ2 ft/sec², are treated exactly the same asĬoefficients with variables, like 16.2 x or Which lets you type an expression using the You’ve just come here to do a particular conversion and you don’t careĪbout the method, I recommend Google Calculator, You can do anyĬonversion, quickly and reliably. If you use a little algebra, they are easy to answer. Kilometers, the conversion factor is 1.61, butĮverybody finds these questions confusing, not just students. Slower than 60 feet per second? If you want to convert 60 miles to If you’re in a car moving at 60 miles an hour, is that faster or Example 4: square feet to square meters.Example 3: kilometers/hour to meters per second.Example 2: miles per second to miles per hour.Example 1: miles per hour to kilometers per hour.
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