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### Pennies in a Mile

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Date: 04/23/99 at 21:01:01
From: Ann Humphreys
Subject: How many pennies are there in a mile?

Dear Dr. Math,

I teach 4th grade. Our school is doing fund-raisers to help beautify
our playground. One of the committee members asked if I could find out
how many pennies there are in a mile. I guess they are going to have a
contest of some sort. I will continue looking for the answer; however,
I saw this Web site and thought it wouldn't hurt to ask.

Thank you,
Ann
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Date: 04/23/99 at 23:01:33
From: Doctor Peterson
Subject: Re: How many pennies are there in a mile?

Hi, Ann.

I can tell you the math, but you'll have to do the measuring - or
better yet, have your students do it.

Just measure the width (or height, if you'll be stacking the pennies
a mile high) of a penny, then divide 5280 feet by whatever you find.
This is a great activity for a class, and in fact a good way to start
the project. First take one penny, and work out an answer. Then get
100 pennies, and measure them; do the same calculation to see how many
pennies it will take to make a mile. There will probably be a
difference, because you can measure 100 pennies more accurately than a
single penny. Or maybe you have a micrometer that will measure one
penny precisely. Which is better can be a good discussion starter. And
don't forget to try it in metric, too.

Just to illustrate, using a very rough estimate of a penny's width,
let's say a penny is about 3/4 inch wide. The number of pennies in a
mile will be

5280 ft   12 in   1 penny
1 mile * ------- * ----- * ------- = 5280 * 12 * 4/3 pennies
1 mi      1 ft   3/4 in

This gives about 84,480 pennies. (This method of doing calculations
with units is very helpful, and would be worth teaching.)

If we measure 100 pennies as 6 ft 1 in, we will get

5280 ft   100 pennies
1 mile * ------- * ----------- = 5280 * 100 * 12 / 73 pennies
1 mi     6 1/12 ft

This gives us 86794.5205 pennies in a mile. Which is more accurate?
Ask the students, and see what ideas they come up with.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Elementary Measurement
Elementary Terms & Units of Measurement
Middle School Measurement
Middle School Terms/Units of Measurement

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