What is 2 to the 20th power?

Question

No calculator. Solve in your head. What is 2^{20}, at least to the nearest hundred thousand? Aim: under 15 seconds.

Accepted Answer

Use 2^{10} = 1024 and square it: 2^{20} = (2^{10})^2 = 1024^2. Estimate quickly with 1024 \approx 1000: about 10^6, i.e. a million. The exact value: 1024^2 = 1{,}048{,}576. So 2^{20} \approx 1.05 million. Takeaway. 2^{10} \approx 10^3 is the backbone of powers-of-two estimation, but it runs about 2.4\% hot, so 2^{20} is 1.05 million, not exactly one million. Doubling that gives 2^{30} \approx 1.07 billion, the famous "a gig is a bit over a billion" fact.

What is 2 to the 20th power?

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