Bot GPT 3.5

Question

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Bot GPT 3.5
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.

Answer 1

To convert a recurring decimal like 0.72¯¯¯¯¯ to a rational number, we can use the concept of geometric series. Let x = 0.72¯¯¯¯¯, then 100x = 72.72¯¯¯¯¯.

Subtracting these two equations, we get:

100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
x = 72/99

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:

(72/9) / (99/9) = 8/11

Therefore, the rational number equivalent to 0.72¯¯¯¯¯ in simplest form is 8/11.

Answer 2

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Answer 3

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