4400 Higher June 2006 Paper 3 Q17
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)
| Scheme | Marks |
|---|---|
| (i) e.g. 9 | B1 |
| (ii) multiple of 9 | B1 |
| (2) |
Notes
B1: Accept any multiple of 9 inc 45, 90, …
Must be positive whole number
B1: Accept ‘in 9 times table’ oe
| Scheme | Marks |
|---|---|
| 1.3777… and 1.4222… | M1 |
| 1.4 and agree to 2 sf or 1 dp oe | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for converting to decimals with at least 2 dp rounded or truncated
A1: 1.4 and correct explanation needed