Convert 0.454545... (0.4̄5̄) to a rational number.
GeneralClass 12AllAnswered 27 Mar 2026
Answer
Step 1: Let x = 0.454545...
Step 2: Since 2 digits repeat, multiply by 100
- 100x = 45.454545...
Step 3: Subtract
100x - x = 45.454545... - 0.454545...
99x = 45Step 4: Solve
x = 45/99Step 5: Simplify (GCD = 9)
45/99 = 5/11Answer: 0.4̄5̄ = 5/11
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