The decimal 0.̅6 is equal to which fraction?
Answer and explanation
Correct answer: 2/3
The governing concept is conversion of a recurring decimal into a fraction. Let x = 0.666..., where the digit 6 repeats indefinitely. Multiplying by 10 gives 10x = 6.666... . Subtracting the original equation from this one removes the repeating decimal: 10x - x = 6.666... - 0.666..., so 9x = 6 and x = 6/9 = 2/3. Therefore option B is correct. The shortcut gives the same result: one repeating digit is written over 9, so 0.̅6 = 6/9, which simplifies to 2/3. The other options have different values and do not represent the repeating decimal.
Frequently asked questions
What is the correct answer to this question?
2/3
Why is this the correct answer?
The governing concept is conversion of a recurring decimal into a fraction. Let x = 0.666..., where the digit 6 repeats indefinitely. Multiplying by 10 gives 10x = 6.666... . Subtracting the original equation from this one removes the repeating decimal: 10x - x = 6.666... - 0.666..., so 9x = 6 and x = 6/9 = 2/3. Therefore option B is correct. The shortcut gives the same result: one repeating digit is written over 9, so 0.̅6 = 6/9, which simplifies to 2/3. The other options have different values and do not represent the repeating decimal.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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