4400 Higher June 2006 Paper 3 Q17

EdexcelHigherOld spec4 marksRecurring DecimalsUpper & Lower Bounds

17 Michael says \(\quad\) “When the fraction \(\dfrac{n}{45}\) is converted to a decimal, it never gives a terminating decimal.”

(a)
(i) Find a value of \(n\) which shows that Michael is wrong.
(ii) Write down the name of the type of number \(n\) must be, when \(\dfrac{n}{45}\) gives a terminating decimal. (2)
(b) \(\dfrac{62}{45} < \sqrt{2} < \dfrac{64}{45}\)

Use these bounds to write the value of \(\sqrt{2}\) to an appropriate degree of accuracy.
You must show your working and explain your answer.

(2)

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