Pennies in a Mile

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

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/