IMC 2008 Q18
18. In the calculation 1003 ÷ 4995 = \(0.2\dot{0}0\dot{8}\), the number \(0.2\dot{0}0\dot{8}\) represents the recurring decimal fraction 0.2008008008008… . When the answers to the following calculations are arranged in numerical order, which one is in the middle?
- A 226 ÷ 1125 = \(0.200\dot{8}\)
- B 251 ÷ 1250 = 0.2008
- C 497 ÷ 2475 = \(0.20\dot{0}\dot{8}\)
- D 1003 ÷ 4995 = \(0.2\dot{0}0\dot{8}\)
- E 2008 ÷ 9999 = \(0.\dot{2}00\dot{8}\)
Intermediate Mathematical Challenge 2008, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 497 ÷ 2475 = \(0.20\dot{0}\dot{8}\)
The five options are: A 0.20088888… B 0.20080000… C 0.20080808… D 0.20080080… E 0.20082008….
So in ascending order they are B D C E A.
Solution © UK Mathematics Trust, from the IMC 2008 solutions.