4400 Higher November 2008 Paper 3 Q17
17
(a) Convert the recurring decimal \(0.\dot{7}\) to a fraction. (2)
\(0.0\dot{y}\) is a recurring decimal.
\(y\) is a whole number such that \(1 \leqslant y \leqslant 9\)
(b)
(i) Write the recurring decimal \(0.0\dot{y}\) as a fraction.
(ii) \(0.1\dot{y}\) is also a recurring decimal.
Using your answer to part (i), or otherwise, convert the recurring decimal \(0.1\dot{y}\) to a fraction.
Give your answer as simply as possible.
(3)Using your answer to part (i), or otherwise, convert the recurring decimal \(0.1\dot{y}\) to a fraction.
Give your answer as simply as possible.
| Scheme | Marks |
|---|---|
| \(10x = 7.\dot{7}\) | M1 |
| \(\frac{7}{9}\) oe | A1 |
| (2) |
Notes
M1: Accept \(100x = 77.\dot{7}\)
| Scheme | Marks |
|---|---|
| (i) Answer: \(\frac{y}{90}\) | B1 |
| (ii) eg \(9d = 1 + \frac{y - 1}{10}\) or \(90d = 10 + y - 1\) or \(90d = y + 9\) or \(\frac{10 + y - 1}{90}\) or \(0.1 + 0.0\dot{y}\) | M1 |
| \(\frac{9 + y}{90}\) or \(\frac{1}{10} + \frac{y}{90}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for equation which would give a correct answer or for an expression which, if simplified would give a correct answer or for \(0.1 + 0.0\dot{y}\)
but not for \(9d = 1.y - 1\) or similar
A1: isw and award 2 marks if \(\frac{9 + y}{90}\) or \(\frac{1}{10} + \frac{y}{90}\) seen