Write 2/7 as a decimal

Question

Solve in your head, no long division. What is 	frac{2}{7} as a decimal (first six digits)? Aim: under 15 seconds.

Accepted Answer

Every seventh reads off the single wheel 142857; you just pick the right starting point by size. 	frac{2}{7} \approx 0.29 \quad (	ext{since } 2 	imes 14.3\% \approx 29\%). Rotate 142857 to the block that starts near 29: that is 285714. 	frac{2}{7} = 0.\overline{285714}. Check: 7 	imes 0.285714 = 1.999998, correct to rounding. Unlike the thirteenths, the sevenths need only one wheel, all six fractions are rotations of 142857, so once you size the fraction the rotation is forced. Takeaway. For 	frac{k}{7}: multiply k by 14.3\% for the first two digits, then read the matching rotation of 1…

Write 2/7 as a decimal

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