Hint
Use the stated units and precision. Shift to align the recurring tails, subtract, then reduce the resulting exact fraction.
Worked solution
(a)
\(10X=3+Y\). Also \(10Y-Y=4\), so \(\displaystyle Y=\frac{4}{9}\). Therefore \(\displaystyle X=\frac{31}{90}\).
Answer: \(\displaystyle \frac{31}{90}\)
(b)
\((10-1)Y=4\) gives \(\displaystyle \frac{4}{9}\).
Answer: \(\displaystyle \frac{4}{9}\)
(c)
Shift to align the recurring tails, subtract, then reduce the resulting exact fraction.
\(\displaystyle \frac{4}{9}\)
Answer: \(\displaystyle \frac{4}{9}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 3 marks
- 1 mark: Use powers of ten to align and eliminate the identical recurring tails.
- 1 mark: Account for the non-repeating prefix and simplify the complete fraction.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Subtract two correctly scaled equations and reduce the resulting fraction.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Shift to align the recurring tails, subtract, then reduce the resulting exact fraction.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 7 marks.