Higher June 2022 Paper 1 Q12
12 Express \(0.1\dot{1}\dot{7}\) as a fraction.
You must show all your working. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{116}{990}\) | M1 | for \((x =)\ 0.11717\ldots\) or \((10x =)\ 1.\dot{1}\dot{7}\) or \(1.1717\ldots\) or \((100x =)\ 11.\dot{7}\dot{1}\) or \(11.7171\ldots\) or \((1000x =)\ 117.\dot{1}\dot{7}\) or \(117.1717\ldots\) |
| M1 | (dep M1) for a method using two recurring decimals that leads to a terminating decimal difference, using correct multiples of \(x\) eg \((1000x - 10x =)\ 117.\dot{1}\dot{7} - 1.\dot{1}\dot{7}\ (= 116)\) or \(117.1717\ldots - 1.1717\ldots\ (= 116)\) | |
| A1 | for \(\dfrac{116}{990}\) oe, eg \(\dfrac{58}{495}\) |
Additional guidance
Accept
\((100x - x =)\ 11.\dot{7}\dot{1} - 0.1\dot{1}\dot{7}\)
or \(11.7171\ldots - 0.11717\ldots\ (= 11.6)\)
\(\dfrac{11.6}{99}\) must be written in the form \(\dfrac{a}{b}\) where \(a\) and \(b\) are integers to gain the accuracy mark