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13 (a) Write \( \frac{7}{9} \) as a recurring decimal - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Question 13
13 (a) Write \( \frac{7}{9} \) as a recurring decimal. (b) Sally divided a two-digit number by another two-digit number. Her answer was 3.181818...... Find two num... show full transcript
Worked Solution & Example Answer:13 (a) Write \( \frac{7}{9} \) as a recurring decimal - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Step 1
Step 2
Sally divided a two-digit number by another two-digit number. Her answer was 3.181818......
Answer
Sally's answer can be expressed as ( 3.18 \overline{18} ). To find the two two-digit numbers, note that the non-recurring part '3' indicates the divisor is close to 3.
- Consider the equation: [ \text{Dividend} = 3.18 \overline{18} \times \text{Divisor} ]
- Solving for two-digit possibilities, one pair is:
- 35 (as the dividend) and 11 (as the divisor), where ( 35 \div 11 = 3.181818... ).
- Another possible pair is:
- 22 (as the divisor) and 70 (as the dividend), since ( 70 \div 22 = 3.181818... ).
- Therefore, two valid numbers are 35 and 11, or 70 and 22.