Comparing 2 Numbers

Which is larger? 10³⁶ or 9³⁷? And how I compare them.

Strategy

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Here’s the strategy: Compare them with 1.

Just divide them and get the result. If the result is larger than 1, then A is larger than B.

My Steps

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In this case, I’ll assign them as below:

A = 9³⁷

B = 10³⁶

Instead of A = 10^36, I use A = 9^37 because it is easier to compare.

Let’s simplify A first:

A = 9³⁷ = 9³⁶ * 9

So,

A / B = (9³⁶ * 9) / (10³⁶) = (0.9)³⁶ * 9

Obviously, the result is smaller than 1.

And the conclusion is 10³⁶ > 9³⁷.