A number is considered rational if it can be expressed as the ratio of two integers (i.e., in the form \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \)).
Let's evaluate each of the given options:
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0.23242526...
- This is a non-repeating, non-terminating decimal, which is not rational.
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\( \frac{\sqrt{2}}{4} \)
- Although \( \sqrt{2} \) is irrational, this number can be expressed as the ratio of two numbers (where the numerator is an irrational number). Therefore, this is not a rational number because the square root of 2 itself does not yield a rational result.
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\( \sqrt{15} \)
- The square root of 15 is also irrational since 15 is not a perfect square. Thus, it is not rational.
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0.98989898...
- This is a repeating decimal (0.98 repeating). Repeating decimals can be expressed as fractions, making this a rational number.
So the rational number from the given options is 0.98989898....
1 answer