What is 5/6 as a percentage?

Question

Sixths give repeating decimals, but a tidy one. Solve in your head. What is 	frac{5}{6} as a percentage? Aim: under 10 seconds.

Accepted Answer

Anchor on 	frac{1}{6} = 0.1\overline{6} = 16.\overline{6}\%. Then 	frac{5}{6} = 5 	imes 16.\overline{6}\% = 83.\overline{3}\%. Sanity check the other way: 	frac56 = 1 - 	frac16 = 100\% - 16.\overline{6}\% = 83.\overline{3}\%. Takeaway. The sixths alternate their repeating tail: 	frac16 = 16.\overline6\%, 	frac26 = 33.\overline3\%, 	frac36 = 50\%, 	frac46 = 66.\overline6\%, 	frac56 = 83.\overline3\%. Memorising 	frac16 \approx 16.7\% and using the complement makes the top ones trivial.

What is 5/6 as a percentage?

Your answer

More Mental Math questions