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Convert the repeating decimal 0.45̄ (45 repeating: 0.454545…) to the form p/q:
A45/100
B5/11
C9/20
D45/99
Answer & Solution
Correct answer: B. 5/11
Let x = 0.4545454545… Two digits repeat, so multiply by 100: 100x = 45.4545… Subtract: 100x − x = 45.4545… − 0.4545… = 45. So 99x = 45, giving x = 45/99 = 5/11 (after dividing both by 9). Verify: 5/11 = 0.454545… ✓
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