Matching Fractions, Decimals and Percentages

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

Sept 03

What is the last digit of the number 1 / 5^903 ?

Too Close to Call

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

Round and Round and Round

Age 11 to 14Challenge Level
This problem follows on from Going Round in Circles.
Watch the film below.

Imagine the dot starts at the point $(1,0)$, turns through $60$ degrees anticlockwise and then stops.

I was wondering, if the point hadn't stopped, and instead carried on until it had turned through $30$ $000$ degrees, might it have finished the same distance above the horizontal axis?

I took out my calculator and typed $30$ $000$ $\div$ $360$
The answer on the screen was $83.333333$.

How can I use this to help me solve my problem?

There are ideas for follow-up problems in the Notes .