Write 3/7 as a decimal

Question

Solve in your head, no long division. What is 	frac{3}{7} as a decimal (first six digits)? Aim: under 15 seconds.

Accepted Answer

All sixths of a seventh live on one wheel, the digits 142857 read cyclically. To find which rotation, estimate the size and read off the block that starts near it. 	frac{3}{7} \approx 0.43 \quad (	ext{since } 3 	imes 14.3\% \approx 43\%). Spin the wheel 142857 to the rotation beginning near 43: that is 428571. 	frac{3}{7} = 0.\overline{428571}. Check: 7 	imes 0.428571 = 2.999997, correct to rounding. For reference the full wheel is 	frac{1}{7}=0.\overline{142857}, 	frac{2}{7}=0.\overline{285714}, 	frac{3}{7}=0.\overline{428571}, 	frac{4}{7}=0.\overline{571428}, 	frac{5}{7}=0.\overli…

Write 3/7 as a decimal

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