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Repetitiously

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Sept 03

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

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Too Close to Call

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

Round and Round and Round

Stage: 3 Challenge Level: Challenge Level:1
This problem follows on from Going Round in Circles.
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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 .