Discussion
The equivalent value of \(6.5\overline{34}\) is:
Answer: B
The value is \(6\frac{529}{990}\). The number 6.5\(\overline{34}\) has one non-repeating digit (5) and two repeating digits (34). For such a decimal the fraction is the number formed by all the digits after the point, minus the non-repeating part, over 990. \[0.5\overline{34} = \frac{534 - 5}{990} = \frac{529}{990}\] So the number is \(6\frac{529}{990}\). The denominator 900 would suit a number with two non-repeating digits and one repeating digit, and 999 a purely recurring three-digit block, so those options use the wrong denominators. The option with 531 comes from subtracting wrongly.
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