Final answer:
To write the repeating decimal 0.82 as a fraction, we use the fact that a repeating decimal is equivalent to the fraction formed by the digits in the repetend divided by a number with the same number of nines as digits in the repetend. So, 0.82 can be written as 82/99.
Step-by-step explanation:
To write the repeating decimal 0.82 as a fraction, we use the fact that a repeating decimal is equivalent to the fraction formed by the digits in the repetend divided by a number with the same number of nines as digits in the repetend. In this case, the repetend is 82, which consists of two digits. So, we write it as a fraction with the repetend as the numerator and 99 as the denominator:
0.82 = 82/99
Therefore, the repeating decimal 0.82 can be written as the fraction 82/99.
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