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Question Number 11606 by Joel576 last updated on 29/Mar/17

$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{smallest}\mathrm{positive}\mathrm{integer}x\mathrm{for}$$$$\mathrm{which}\frac{1}{32}=\frac{x}{{10}^y}\mathrm{for}\mathrm{some}\mathrm{positive}\mathrm{integer}y?$$

Answered by mrW1 last updated on 29/Mar/17

$$32x={10}^y={\left(2\times 5\right)}^y=2^y\times 5^y$$$$2^{5}x=2^y\times 5^y$$$$x=2^{y-5}\times 5^y$$$$forxtobepositiveinteger,itmustbe$$$$y-5⩾0ory⩾5$$$$\Rightarrow min.x=2^0\times 5^5=3125$$

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