### Repetitiously

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

### 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

##### Stage: 3 Challenge Level:

This problem offers students an opportunity to test their understanding of division and to consider different ways in which calculators can be used.

The interactivity also offers students a chance to explore the relationships between the angles of turn that produce the same vertical and horizontal displacements.

Imagine the dot starts at the point $(1,0)$, turns through $20$ $000$ degrees anticlockwise and then stops.

Through what angle(s) between $0$ and $360$ degrees would the dot have had to turn if it was to finish the same distance above/below the horizontal axis?

If I type $20$ $000$ $\div$ $360$ into my calculator the answer on the screen is $55.555556$
How can this help me answer the question?

Similarly for $40$ $000$ degrees.
If I type $40$ $000$ $\div$ $360$ into my calculator the answer on the screen is $111.11111$.

Similarly for $80$ $000$ degrees.
If I type $80$ $000$ $\div$ $360$ into my calculator the answer on the screen is $222.22222$.

Similarly for $250$ $000$ degrees.
If I type $250$ $000$ $\div$ $360$ into my calculator the answer on the screen is $694.44444$.

And what about horizontal displacements to the left/right of the vertical axis?

Students could make up their own questions...