Higher November 2018 Paper 6 Q14
14
(a) Without using a calculator, show that \(0.\dot{1}\dot{9}\) can be written as \(\dfrac{19}{99}\). [3]
(b) Explain how \(\dfrac{19}{99} = 0.\dot{1}\dot{9}\) can be used to find \(\dfrac{19}{990}\) as a decimal and write down its value. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(x = 0.191919\ldots\) \(100x = 19.191919\ldots\) \(99x = 19\) \(x = \dfrac{19}{99}\) | 3 | M1 for \(100x = 19.191919\ldots\) and M1 for \(100x - x = 19.191919\ldots - 0.191919\ldots\) or better | For full marks, clear step by step process must be evident Apply marks in a similar way to other methods e.g. M1 and M1 for \(10000x - 100x = 1919.1919\ldots - 19.1919\ldots\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(0.\dot{1}\dot{9} \div 10\) or “divide by 10” | 1 | ||
| \(= 0.0\dot{1}\dot{9}\) | 1 dep | Dependent on first mark | Answer only scores 0 |