IMC 2017 Q8
8. Which of the following numbers is the largest?
- A 1.3542
- B \(1.354\dot{2}\)
- C \(1.35\dot{4}\dot{2}\)
- D \(1.3\dot{5}4\dot{2}\)
- E \(1.\dot{3}54\dot{2}\)
Intermediate Mathematical Challenge 2017, Question 8. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D \(1.3\dot{5}4\dot{2}\)
Consider options B to E: \(1.354\dot{2} = 1.354222 \ldots\) ; \(1.35\dot{4}\dot{2} = 1.35424242 \ldots\) ; \(1.3\dot{5}4\dot{2} = 1.3542542 \ldots\) ; \(1.\dot{3}54\dot{2} = 1.35423542 \ldots\) . These are all greater than 1.3542, so option A is not correct. The other four options have the same units digit and the first four digits after the decimal point are the same in all. So the largest option is that which has the largest digit five places after the decimal point and this is \(1.3\dot{5}4\dot{2}\).
Solution © UK Mathematics Trust, from the IMC 2017 solutions. Longer versions with investigations: Solutions and investigations (PDF).