10 (a) Write 1/6 as a recurring decimal - OCR - GCSE Maths - Question 12 - 2019 - Paper 5

To determine whether Elsa is correct, we first consider the division she performed:

Let the two-digit number be represented as $x$ and the divisor as $y$. Then:

$\frac{x}{y} = 0.15$

This can be rearranged to:

$x = 0.15y$

Multiplying through by 100 to eliminate the decimal gives:

$100x = 15y$

This simplifies to:

$20x = 3y$

For $y$ to be a two-digit number, $x$ must be a multiple of 3 to ensure $y$ remains an integer. The two-digit multiples of 20 ($20, 40, 60, 80$) yield the corresponding two-digit values for $y$.

Calculating:

• For $x = 20$, y = rac{20 imes 3}{20} = 60
• For $x = 40$, y = rac{40 imes 3}{20} = 120
  (Not valid as it exceeds two digits)
• For $x = 60$, y = rac{60 imes 3}{20} = 90
• For $x = 80$, y = rac{80 imes 3}{20} = 120
  (Still not valid)

Thus, the pairs $(20, 60)$ and $(60, 90)$ satisfy the equation. Hence, Elsa is incorrect, as there are at least two pairs that yield 0.15.