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Question Number 16944 by Tinkutara last updated on 28/Jun/17

Find the number of digits in the  number 2^(2005)  × 5^(2000)  when written in  full.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{2}^{\mathrm{2005}} \:×\:\mathrm{5}^{\mathrm{2000}} \:\mathrm{when}\:\mathrm{written}\:\mathrm{in} \\ $$$$\mathrm{full}. \\ $$

Commented by RasheedSoomro last updated on 28/Jun/17

2^(2005) ×5^(2000)   =2^5 ×2^(2000) ×5^(2000)   32×(2×5)^(2000)   32×10^(2000)   Two digits of 32 and 2000 zeros  Total digits 2002

$$\mathrm{2}^{\mathrm{2005}} ×\mathrm{5}^{\mathrm{2000}} \\ $$$$=\mathrm{2}^{\mathrm{5}} ×\mathrm{2}^{\mathrm{2000}} ×\mathrm{5}^{\mathrm{2000}} \\ $$$$\mathrm{32}×\left(\mathrm{2}×\mathrm{5}\right)^{\mathrm{2000}} \\ $$$$\mathrm{32}×\mathrm{10}^{\mathrm{2000}} \\ $$$$\mathrm{Two}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{32}\:\mathrm{and}\:\mathrm{2000}\:\mathrm{zeros} \\ $$$$\mathrm{Total}\:\mathrm{digits}\:\mathrm{2002} \\ $$

Commented by Tinkutara last updated on 29/Jun/17

Thanks Sir!

$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$

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