This technique, now known as a “Fermi Estimate,” works by estimating numbers in powers of ten (see TED-Ed video above for more). So when trying to come up with a seemingly impossible solution, it helps to chunk items in this way and then break them down. For example, when trying to estimate the number of piano tuners in your city, first estimate the population of your city (e.g. 1,000,000), then estimate the number pianos (10,000), and then the number of piano tuners (e.g. 100). You won’t get the actual answer, but you’ll get an answer quickly, and one that’s often close enough.

### When in Doubt, Rearrange

It’s a good idea to use the rules of math to rearrange complex problems into a simpler form. For instance, computing the problem 5x(14+43) is a daunting task on it’s own, but it can be broken down into three fairly manageable calculations. Remembering your order of operations, this problem can be rephrased as (5x14) + (5x40) + (5x3) = 285.

### Turn a Big Problem Into a Bunch of Small Ones

When in doubt, decompose. “For many problems, the way to do them fast is to break them into subproblems and solve those,” says Greenberg. “When you get a problem that sounds hard, it’s often fruitful to look for ways that it can be broken apart into easier problems that you already know how to solve.”

For instance, you can multiply by 8 by doubling three times. So instead of trying to figure out 12x8, just double 12 three times: 24, 48, 96. Or when multiplying by 5, I start by multiply by 10 since it’s easy, then divide by 2 since that’s also usually pretty easy. For example, for 5x18, calculate 10x18 instead, and divide by 2, where 180/2=90.

### Use Scientific Notation For Unreasonably Large Numbers

When calculating large numbers in your head, remember that you can convert them into scientific notation first. What’s 44 billion divided by 400,000? A simple way to deal with this is to convert 4 billion to 109, and 400,000 to 105. We can now express this as 44/4 and 109/105. As Greenberg points out, the rule for dividing exponents requires us to subtract them (easy!), so we get 11 x 10(9-5)= 11 x 104 = 110,000.

### The Simplest Way to Calculate the Tip

Finally, some advice on how to calculate a tip in your head. If you can calculate a 10 percent tip in your head (easy), then you can calculate both a 20 percent tip and a 15 percent tip.