Question
\( 1 \leftarrow \) Convert the following rational number into either a repeating or a terminating decimal. Use a calculator if allowed. Choose the correct answer below. A. \( 0 . \overline{6} \) B. 0.6 C. \( 6 . \overline{6} \) D. \( 2 . \overline{6} \)
Ask by Floyd Parry. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The decimal representation of \( \frac{2}{3} \) is \( 0.\overline{6} \).
Solution
To convert the rational number into a decimal, we need to perform the division of the numerator by the denominator. However, since the rational number is not provided in your question, I will assume you meant to convert the fraction \( \frac{2}{3} \) into a decimal, as it is a common example that results in a repeating decimal.
Let's perform the division:
1. Divide \( 2 \) by \( 3 \):
- \( 2 \div 3 = 0.6666... \)
This indicates that the decimal representation of \( \frac{2}{3} \) is \( 0.6 \) with the \( 6 \) repeating indefinitely.
Thus, the correct answer is:
A. \( 0 . \overline{6} \)
If you meant a different rational number, please provide it, and I can assist you further!
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Simplify this solution Bonus Knowledge
To convert the rational number into a decimal, you can divide the numerator by the denominator. For example, if your rational number is \( \frac{2}{3} \), dividing gives you \( 0.666...\), which is the same as \( 0.\overline{6} \). This indicates a repeating decimal where the 6 repeats infinitely. In contrast, if your rational number is \( \frac{1}{2} \), it produces a terminating decimal of \( 0.5 \). The options presented suggest a number like \( \frac{2}{3} \), leading us to the conclusion that the answer is \( 0 . \overline{6} \), which corresponds to option A!
