Number Theory

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Find the six-digit number abcdef such that
0.\overline{abcdef} = \frac{2}{17},
without a calculator.

gnistory Jun 18, 2024

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Best Answer

+1926

+1

We can use simple long division to solve this problem.

We have that \(2/17 = 0.\overline{1176470588235293}\)

There are 16 digits repeating in this decimal.

So our answer is 1176470588235293.

I'm not sure how there's only 6 digits, but there are 16 digit repeating.

Thanks! :)

NotThatSmart Jun 18, 2024

1⁺⁰ Answers

+1926

+1

Best Answer

We can use simple long division to solve this problem.

We have that \(2/17 = 0.\overline{1176470588235293}\)

There are 16 digits repeating in this decimal.

So our answer is 1176470588235293.

I'm not sure how there's only 6 digits, but there are 16 digit repeating.

Thanks! :)

NotThatSmart Jun 18, 2024

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