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\( \mid \leftarrow \) Convert the following rational number into either a repeating or a terminating decimal. Use a calculator if allowed. \( \frac{83}{99} \) Choose the correct answer below. A. 0.83 B. \( 83 . \overline{83} \) C. \( 0 . \overline{83} \) D. \( 99 . \overline{83} \)

Ask by Chan Black. in the United States
Mar 10,2025

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The decimal form of \( \frac{83}{99} \) is \( 0.\overline{83} \), which is option C.

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To convert the rational number \( \frac{83}{99} \) into a decimal, you can divide 83 by 99. Upon doing this, you will find that it results in a repeating decimal. Specifically, the decimal representation will be \( 0.\overline{83} \), indicating that the digits "83" repeat indefinitely. Thus, the correct answer is: C. \( 0 . \overline{83} \) For those interested in mathematical tidbits, note that fractions like this one can be examined through their decimal expansions. When the denominator has prime factors different from 2 and 5, like 99 (which is \( 3^2 \times 11 \)), you're more likely to get a repeating decimal! It’s a neat trick to remember!

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