About nine trillion snowflakes fell on Prexy’s Pasture during the recent storm.
The techniques I used to estimate this—without a calculator—are something everyone can use. Even if you don’t like math, getting comfortable with estimates and approximations can help anybody with everyday jobs like shopping, balancing checkbooks or telling politicians how ridiculous they are.
First, let’s think about the problem. After the storm, Prexy’s was covered with snow. We could figure out how much by knowing the area of Prexy’s and the depth of snow. Then, if we knew the size of a typical snowflake, we could estimate the number of snowflakes in that volume.
This is the most important step. We don’t have the answer yet, but we know how to find it. We’ve connected what we want to figure out (the number of snowflakes) to information we can estimate (the depth of snow, the area of Prexy’s and the size of a snowflake).
I estimate each snowflake took up one cubic millimeter of volume. In case you’re not familiar with the metric system, there are about 25 millimeters in an inch. Ten millimeters make a centimeter and 100 centimeters make a meter, which is about three feet. Those nice factors of ten make it easier to do quick calculations in the metric system.
The campus map shows Prexy’s has a width of about one and a half blocks and a length of around two blocks. A quick Google search shows a city block is about 100 meters, so Prexy’s is around 150 by 200 meters. While these numbers aren’t perfectly accurate, that’s fine because we just want a rough estimate.
Multiplying length and width gives area, and a calculator is unnecessary: 15 times two is 30, and then there are three more zeros, so the area is around 30,000 square meters.
I’d say we got about 30 centimeters (around a foot) of snow. To find the volume, we multiply the 30,000 square meters of area by 0.3 meters of snow thickness. Again, no calculator is needed: three times three is nine, there are four zeros with the first number and one decimal place on the second, so the volume is 9,000 cubic meters.
Now we’re ready to find the number of snowflakes. Since one meter has 1,000 millimeters, a cube measuring one meter on each side contains (1000)*(1000)*(1000) or 1,000,000,000 (one billion) cubic millimeters. This means there were about 9,000,000,000,000 or nine trillion cubic millimeters. Each snowflake was one cubic millimeter; so about nine trillion snowflakes fell on Prexy’s Pasture.
The real answer might be ten trillion or eight trillion. However, unless one of our estimates is a thousand times too big, we know it’s definitely closer to nine trillion than to nine billion.
If you know the times table and can multiply by ten, you can do estimates. That means all college students can do it, whether you think of yourself as a “math person” or not. It doesn’t take magical ability to visualize a problem, make some approximations and do arithmetic, but it’s a great way to look smart.
