Ben Bradlee: Garage Freak? Jesus, what type of a crazy f*****g story is this? that did girlfriend say?
Howard Simons: He"s on deep background, I speak to him deep... Throat.
Here"s what we did therefore far:
Let"s take the a little an ext slowly.
How the heck is multiplying by 5280 feet ⁄ 1 mile the exact same as multiplying by 1?
It"s simple to check out why fractions favor 2 ⁄ 2 work, however not so straightforward with 5280 feet ⁄ 1 mile.
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In fact, if friend didn"t have actually the units there, that WOULDN"T work. Clearly, 5280 ⁄ 1 does no equal 1!!
But, with the units, we understand that the top and the bottom actually room the same. That"s because 5280 feet actually are the exact same as 1 mile. Therefore this portion is the same as 1.
OK, however that means that multiply by 1 mile ⁄ 5280 feet would additionally be the exact same as multiplying by 1, right?
Right! also if you upper and lower reversal the fraction, it will still be same to 1. But (as we"ll view in a minute) some fractions-that-equal-1 are a lot an ext useful 보다 others.
But still, why would I want to carry out this?
Because it allows you to convert units.
For example, once you"re in liven parking garage, 4.5 mile doesn"t sound choose much. It sounds a bit much better in feet though:
Wait, how did you do "miles" walk away?
Here"s the yes, really cool thing: you deserve to cancel out units in fractions specifically LIKE girlfriend cancel out numbers. So, the mile cancel out, and you room left with kilometers only.
So, since 5280 feet ⁄ 1 mile and 1 mile ⁄ 5280 feet space both equal to 1, exactly how do I recognize which one come choose?
Remember, you should cancel out the miles, for this reason pick the one the does the trick. Follow the units!! But, no worries: if you pick the dorn one, you"ll an alert when you shot to get the final answer:
4 mile * 1 mile ⁄ 5280 feet = ??? miles2/ft.
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Gaack! miles2/ft is definitely not the units you to be going for!! If this happens, it"s probably since you have to flip a portion to do the units occupational out. Simply make certain you upper and lower reversal BOTH the numbers and also the units!
Hey, wait a minute, I already know just how to convert miles and also feet. Why space you do the efforts to do me learn a new method???!
Yup, so carry out I:
miles * 5280 -> feet, or
feet / 5280 -> miles
The trouble is, occasionally I forget i beg your pardon one I"m supposed to multiply, and which one i divide. The fraction method is much much more forgiving. Every I should remember is that 1 mile = 5280 feet. From there, i can construct the portion I need, and if ns goof up, it"s evident because the devices don"t job-related out.
So room you informing me the a scientist v a labcoat and a supercomputer would look increase conversion factors and also write equations? Wouldn"t they simply use a computer for that??
No, castle wouldn"t "just usage a computer," because there"s no easy means to perform that - in fact, ns look increase conversion factors all the moment (and I have a few memorized). Utilizing these equations is second nature for me. (Now, utilizing pencil and paper rather than a calculator or a spreadsheet - that is truly crazy! use those electronics, people! It"s not favor we"re earlier in the 1960"s.)
So you use a large book of switch tables? Where perform you save it, under your pillow?
No, commonly I just use Google, prefer this: