### How To Measure The Thickness Of A single Page With Only A 12 Inch Ruler

Some things seem impossible until we are first shown how. If you were asked to measure the thickness of one page in a textbook using only a common twelve inch ruler you may argue that it can't be done. The divisions on the ruler are simply too big to measure something as thin as the thickness of one sheet of paper. However, it can be done, and rather accurately too.

Here is a strategy we can use to measure a single sheet of paper with a common ruler. We will assume that all the pages in our textbook are the same thickness. While we cannot measure a single page, we can measure a bunch of them at a time with a ruler. Suppose we measure a stack of pages that is exactly one inch thick. If we were to count the number of pages in this stack, and then divide the thickness of the stack by the number pages in the stack we will be able to calculate the thickness of a single sheet.

To find the number of pages in a one inch stack we could count them, but there is an easier way. Suppose we start our stack on page one and find that the last page in our one inch thick stack is page 538. We might at assume that there were 538 sheets in our stack, but we would be wrong if we did. "Why?", because there are two numbers on each sheet, one on the front, and another on the back. So, if we start with 1 and end with page number 538, there are half as many sheets in the stack as there are page numbers, or 538/2 which equals 269.

In this example there are 269 sheets in a one inch thick stack. To find the thickness of one page we divide the one inch into 269 pieces. The result is the thickness of one page. In our example, after dividing 1 by 314 we arrive at 0.0037 inches! We did it! We measured the thickness of single page in a book with an ordinary ruler.

"Not so fast!", you say. Is there an accurate way to measure a single page? If so, how close did we come? There is, and we were in good agreement. The tool is called a dial caliper, and as you can see, we came very close. The dial caliper reads 0.0035 inches. Our measurement with a ruler resulted in a value of 0.0037 inches. The difference is only 2 ten-thousandths of an inch. That is very close!