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Repetitiously

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

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Sept 03

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

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Fractions and Percentages Card Game

Match the cards of the same value.

Too Close to Call

Age 11 to 14 Short Challenge Level:

Answer: $\frac{111110}{111111} < \frac{333331}{333334} < \frac{222221}{222223}$

  
$$\frac{111110}{111111} = 1 - \frac{1}{111111} = 1 - \frac{6}{666666}$$ $$\frac{222221}{222223} = 1 - \frac{2}{222223} = 1 - \frac{6}{666669}$$ $$\frac{333331}{333334} = 1 - \frac{3}{333334} = 1 - \frac{6}{666668}$$ Now, $$\frac{6}{666669} < \frac{6}{666668} < \frac{6}{666666}$$ and so

$$\frac{111110}{111111} < \frac{333331}{333334} < \frac{222221}{222223}$$



This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.