Convert 0.45 into the form pq.

Step-by-step solution

Idea: Two digits repeat, so multiply by 10² = 100 to move one whole block in front of the decimal point; the tails then match and cancel.

1. Let x = 0.45 = 0.4545…½ mark
2. Two digits repeat, so multiply by 10² = 100: 100x = 45.45.½ mark
3. Subtract: 100x − x = 45, so 99x = 45.½ mark
4. x = 4599 = 511 (divide by 9).½ mark

Check: 5 ÷ 11 = 0.4545… ✓.

Answer to write in the exam

Common mistakes that cost marks

• Multiplying by 10 for a two-digit block: 10x = 4.5454… does not line up with x = 0.4545…, so the tails do not cancel.
• Writing 99x = 45.45 by subtracting only part of the decimal.
• Stopping at 4599 without reducing to 511.

How this can come in the exam

Try one yourself

Convert 0.81 into the form pq.

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