Higher November 2023 Paper 1 Q19
19 When converted to a fraction \(\quad 0.\dot{7} = \dfrac{7}{9}\)
Work out \(\quad 0.\dot{4} + 0.0\dot{7}\)
Give your answer as a fraction. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((0.\dot{4} =)\ \dfrac{4}{9}\) or \(10x - x = 4\) or \(9x = 4\) | M1 | oe eg \(100x - x = 44\) or \(99x = 44\) or \(100x - 10x = 40\) or \(90x = 40\) any letter |
| \(\dfrac{7}{9} \div 10\) or \(\dfrac{7}{90}\) or \(10y - y = 0.7\) or \(9y = 0.7\) | M1 | oe eg \(100y - y = 7.7\) or \(99y = 7.7\) or \(100y - 10y = 7\) or \(90y = 7\) any letter |
| \(\dfrac{47}{90}\) | A1 | oe single fraction |
| Alternative method 2 | ||
| \(0.5\dot{2}\) | M1 | oe |
| \(10x - x = 4.7\) or \(9x = 4.7\) | M1dep | oe eg \(100x - x = 51.7\) or \(99x = 51.7\) or \(100x - 10x = 47\) or \(90x = 47\) any letter |
| \(\dfrac{47}{90}\) | A1 | oe single fraction |
Additional guidance
For M marks, allow fractions with decimal numerator or denominator
eg in alt 1, \(\dfrac{0.7}{9}\) scores M1 and in alt 2, \(\dfrac{4.7}{9}\) scores M2