4MA0 Higher January 2016 Paper 4R Q15
15 Use algebra to show that the recurring decimal \(0.2\dot{6} = \dfrac{4}{15}\)
(2)
| Scheme | Marks |
|---|---|
| eg. \(x = 0.2666\ldots\) and \(10x = 2.666\ldots\) or \(10x = 2.666\ldots\) and \(100x = 26.66\ldots\) | M1 |
| show | A1 |
| (2) |
Notes
M1: Two correct decimals that, when subtracted, will leave a non-recurring value with intention to subtract.
Must see a recurring symbol or 3+ sixes.
A1: Must see a fraction prior to seeing \(\dfrac{4}{15}\)
Alternative method
| Scheme | Marks |
|---|---|
| eg. \(x = 0.0666\ldots\) and \(100x = 6.666\) with subtraction | M1 |
| A1 |
Notes
M1: for conversion of \(0.0666\ldots\) to a fraction
A1: for conclusion with all steps seen