Higher June 2024 Paper 6 Q17
17
(a) Without using a calculator, show that \(0.\dot{1}\dot{8}\) can be written as \(\frac{2}{11}\). [3]
(b) Explain how \(\frac{2}{11} = 0.\dot{1}\dot{8}\) can be used to find \(\frac{10}{11}\) as a decimal and write down its value. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(x = 0.1818\ldots\) \(100x = 18.1818\ldots\) \(99x = 18\) \(x = \frac{18}{99} = \frac{2}{11}\) | 3 | M1 for \(100x = 18.1818\ldots\) and M1 for \(100x - x = 18.1818\ldots - 0.1818\ldots\) or better | For full marks, clear step by step process must be evident \(x\) and \(100x\) to same number of dp (min of 2dp) or both to min of 4dp or accept \(x = 0.\dot{1}\dot{8}\) and \(100x = 18.\dot{1}\dot{8}\) Apply marks in a similar way to other methods eg M1 and M1 for \(10000x - 100x\) etc If attempting non-calculator 2÷11: For full marks, need to see all “carry-overs” of 9 and 2 and answer to division of 0.181… M2 for “carry-over” of 9 and 2 and answer to division of 0.18 or M1 for “carry-over” of 9 and answer 0.1… |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(0.\dot{1}\dot{8} \times 5\) or \(\frac{2}{11} \times 5\) or ‘multiply by 5’ oe | 1 | Accept equivalent calculations or words e.g. \(0.\dot{1}\dot{8} \div 2 = 0.\dot{0}\dot{9}\) and \(0.\dot{0}\dot{9} \times 10\) ‘divide by 2 and then multiply by 10’ Working may be to min of 4dp but answer must use recurring notation | |
| = \(0.\dot{9}\dot{0}\) nfww | 1dep | dep on first mark | Answer only scores 0 |