Convert 0.666... (repeating) to a rational number.
GeneralClass 12AllAnswered 27 Mar 2026
Answer
Step 1: Let x = 0.666...
Step 2: Multiply by 10 (one repeating digit)
- 10x = 6.666...
Step 3: Subtract original from multiplied
10x - x = 6.666... - 0.666...
9x = 6Step 4: Solve for x
x = 6/9 = 2/3Answer: 0.666... = 2/3
Verification: 2 ÷ 3 = 0.666... ✓
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