Ex: Determine the Thickness and Weight of a Piece of Paper

How thick is a single sheet of paper? Assume you measure a ream of paper, which contains 500 sheets, and it is 2 1/4 inches thick. Let’s begin by setting
up a rate that compares the thickness to the number of sheets. Since we know 500 sheets has
a thickness of 2 1/4 inches, or 2.25 inches, we’ll set this up as 2.25
inches per 500 sheets. And now to determine the
thickness of one sheet, we want to find the unit rate which should be the number
of inches per one sheet, not 500 sheets. And therefore, we’ll divide both the numerator and denominator by 500. This will produce an equivalent unit rate. So 2.25/500 is equal to .0045 or 0.0045. This should be inches. Of course 500 divided by 500 is one. So this is the thickness per one sheet. So we can say the thickness
of one sheet of paper is 0.0045 inches. Next, how much does one
sheet of paper weigh? Assume a ream of 500
sheets weighs 5 pounds. We want to give the answer
in both pounds and ounces. So again we know that there
are 5 pounds per 500 sheets. Again our goal here is
to find the unit rate for the number of pounds per one sheet. So once again we’ll divide both the numerator and denominator by 500 to produce an equivalent unit rate. Our denominator is just
going to be 1 sheet. Our numerator is going to
be 5 divided by 500 pounds which will be .01 or 0.01 pounds. So each sheet weighs 0.01 pounds. We’re also asked to
convert this to ounces. To do this we’ll use the
conversion 16 ounces=1 pound. So if we have 0.01 pounds,
we can put this over 1 and multiply it by a unit fraction to perform this conversion. Because we want to eliminate pounds, our unit fraction will have
pounds in the denominator and ounces in the numerator. And the conversion is 16 ounces=1 pound. Notice here the units of
pounds simplifies out. Therefore this product will
give us the number of ounces in 0.01 pounds. There should be an L here. Well 0.01 times 16 is equal to 0.16. Therefore each sheet weighs
.01 pounds or 0.16 ounces. I hope you found this helpful.

2 thoughts on “Ex: Determine the Thickness and Weight of a Piece of Paper

  1. " two and one fourth " you mean 2 and a quarter? This is the most complex rubbish I have ever seen. I assume American ?

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