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Scientific American presents Math Dude by Quick & Dirty Tips. Scientific American and Quick & Dirty Tips are both Macmillan companies.

Today we’re going to learn how math makes it easy to estimate things that seem practically impossible to calculate. In particular, since summer is in full swing, we’re going to take math to the beach and think about the age-old question: How many grains of sand are on all of Earth’s beaches? As long time Math Dude fans may recall, we first learned about using math to make estimates when we watched Secret Agent Math daringly calculate how many breaths of air there are in a sealed room. So why are we revisiting this topic? Because learning to combine your brain with math to make estimates is an absolutely invaluable skill—and it’s a skill that’s only developed with practice. Which is exactly what we’re going to do today.

Step 1: Make a Plan Sometimes it’s fun to jump right in and do something without really knowing what you’re doing. And while that kind of spontaneity is great for things like claymation and spur-of-the-moment weekend trips, it’s a really bad idea for tackling math problems. As such, the first thing we need to do today is make a plan for figuring out how many grains of sand there are on Earth’s beaches. I know this might sound like a nearly impossible task, but rest assured that overcoming these seemingly long odds—and the sense of dread they instill in the hearts of otherwise brave souls—is precisely what our plan will do.

The best way to tackle a tough problem like this is to break it down into easier parts. In our case, if we can estimate how many grains of sand there are in a typical volume of beach (say the number of grains per cubic meter), and then estimate what the volume of sand is on all the beaches of the world (say in cubic meters), then all we have to do to find the total number of grains of sand is multiply these two numbers together. Easy, right? Well, okay…perhaps this still isn’t exactly easy. But let’s continue marching bravely forward to see if we can tackle each of these sub-problems on their own, and then to see if this divide-and-conquer approach can help make the seemingly impossible possible.

Jason Marshall, PhD, is a research scientist, author of The Math Dude's Quick and Dirty Guide to Algebra, and host of the Math Dude podcast on Quick and Dirty Tips.