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Which of the following are rational numbers? Select all correct answers. Select all that apply: \( \square 0.7171171117 \ldots \) \( \square 0.0505505550 \ldots \) \( \square 0.6262626262 \ldots \) \( \square \) 4.8 \( \square \sqrt{13} \)

Ask by Craig Rose. in the United States
Mar 17,2025

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The rational numbers are: - \( 0.7171171117 \ldots \) - \( 0.0505505550 \ldots \) - \( 0.6262626262 \ldots \) - \( 4.8 \)

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The Deep Dive

The number \( 0.6262626262 \ldots \) is a repeating decimal, which can be expressed as the fraction \( \frac{62}{99} \), making it a rational number. Similarly, \( 4.8 \) can be represented as \( \frac{48}{10} \) or \( \frac{24}{5} \), confirming its rational nature. The other numbers don't neatly fall under the rational umbrella. Rational numbers are those that can be expressed as a fraction of two integers. Fun fact: the decimal expansions of rational numbers either terminate (like \( 4.8 \)) or repeat (like \( 0.6262626262 \ldots \)). So if you see a number dancing in a decimal form that doesn’t end or repeat, it might just be irrational—like the tumultuous square root of any non-square integer!

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