Be a Magician by Calculating Powers of Two in Your Head

You can quickly calculate powers of two in your head by using the rule: add three zeros for each ten in the power, then multiply by whatever is left. This trick is based on three key facts: 2(a+b) = 2a × 2b, 210 is close to 1000, and knowing the powers of 2 up to 210. By approximating numbers using this rule, you can quickly estimate values like the difference between 243 and 7 trillion or the number of items that can be stored with a 32-bit identifier. The trick may underestimate the true answer by about 2.4% per 210, but it's good enough for quick approximations and can be improved upon by adding an additional quarter percent for each 210 in the calculation.

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