conversions - Conversions There are so many units that you...

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Conversions There are so many units that you can use to express results that you need to become proficient at converting from one to another. Fortunately, there is an easy way to do this and it works every time with no exceptions! You simply multiply by one. (The only question is: which one?) Since 12 in = 1 ft, you can get a one by dividing both sides of the equation by 1 ft, giving 12 in 1 ft = 1 . (Notice that this doesn’t say that 12 = 1.) You use this or any similar factor by noticing that if you multiply anything by one, you don’t change it. It’s easy to see with an example; each factor in parentheses equals one. 1 yr = 1 yr · 365 . 24 days 1 yr · 24 hr 1 day · 60 min 1 hr · 60 sec 1 min = 1 / yr · 365 . 24 / day 1 / yr · 24 / hr 1 / day · 60 / min 1 / hr · 60 sec 1 / min = 365 . 24 · 24 · 60 · 60 · sec = 31556736 sec = 3 . 1557 × 10 7 sec , where there are only 5 significant figures in the result, because that’s the limit on the accuracy of the input data for the number of days in a year. (This is about π × 10 7 seconds — easier to remember.) Another example: 1 mi 1 hr = 1 mi 1 hr 5280 ft 1 mi 1 hr 60 min 1 min 60 sec = 1 / mi 1 / hr 5280 ft 1 / mi 1 / hr 60 / min 1 / min 60 sec = 5280 3600 ft sec . = 1 . 47 ft / sec For an example of what can go wrong, what is one mile in inches?
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