Write 10/13 as a decimal

Question

Solve in your head, no long division. What is 	frac{10}{13} as a decimal (first six digits)? Aim: under 15 seconds.

Accepted Answer

The two thirteenth wheels are: - Cycle A, 076923: used by 	frac{1}{13}, 	frac{3}{13}, 	frac{4}{13}, 	frac{9}{13}, 	frac{10}{13}, 	frac{12}{13}. - Cycle B, 153846: used by 	frac{2}{13}, 	frac{5}{13}, 	frac{6}{13}, 	frac{7}{13}, 	frac{8}{13}, 	frac{11}{13}. Size the fraction: 	frac{10}{13} \approx 0.77 (since 10 	imes 7.7\% = 77\%). The two-digit window "76" appears in cycle A, so rotate 076923 to start there: 	frac{10}{13} = 0.\overline{769230}. Check: 13 	imes 0.769230 = 9.99999, correct to rounding. (Being just under 	frac{12}{13}=0.\overline{923076} and above 	frac{9}{13}=…

Write 10/13 as a decimal

Your answer

More Mental Math questions