Convert 2.4537 into the form pq.

Step-by-step solution

Idea: ’45’ does not repeat (2 digits) and ’37’ repeats (2 digits). Multiply by 10² for the non-repeating part, then by 10² more for one repeating block, and subtract.

1. Let x = 2.4537 = 2.453737…½ mark
2. Two non-repeating digits: multiply by 10² = 100 → 100x = 245.37.½ mark
3. Two repeating digits: multiply by 100 more → 10000x = 24537.37.½ mark
4. Subtract: 10000x − 100x = 24537.37 − 245.37 = 24292, so 9900x = 24292.1 mark
5. x = 242929900 = 60732475 (divide by 4).½ mark

Check: 6073 ÷ 2475 = 2.4537373… ✓.

Answer to write in the exam

Common mistakes that cost marks

• Multiplying by 1000 instead of 10000 for the second step: the block 37 has two digits, so it needs another ×100.
• Reducing 242929900 only by 2 (121464950); both are divisible by 4.
• Subtraction slip: 24537 − 245 = 24292.

How this can come in the exam

Try one yourself

Convert 0.3612 into the form pq.

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