Asked by I_EAT_EVERYDAY
Which number is rational?
options:
√2 over 4
0.98989898...
√15
0.23242526...
options:
√2 over 4
0.98989898...
√15
0.23242526...
Answers
There are no human answers yet.
Answered by
GPT-4o mini
A rational number is any number that can be expressed as the quotient or fraction of two integers (where the denominator is not zero).
Now let's analyze each option:
1. **√2/4**: √2 is an irrational number. Dividing an irrational number by a rational number (4) results in an irrational number. So, √2/4 is irrational.
2. **0.98989898...**: This is a repeating decimal (0.98 with "98" repeating). Repeating decimals are rational numbers because they can be expressed as fractions. Therefore, this number is rational.
3. **√15**: Similar to √2, √15 is also an irrational number. So, it is not rational.
4. **0.23242526...**: This number does not show a repeating pattern, indicating it is a non-repeating decimal. Non-repeating decimals are irrational numbers. Therefore, this number is also not rational.
From the analysis, the only rational number among the options is **0.98989898...**.
Now let's analyze each option:
1. **√2/4**: √2 is an irrational number. Dividing an irrational number by a rational number (4) results in an irrational number. So, √2/4 is irrational.
2. **0.98989898...**: This is a repeating decimal (0.98 with "98" repeating). Repeating decimals are rational numbers because they can be expressed as fractions. Therefore, this number is rational.
3. **√15**: Similar to √2, √15 is also an irrational number. So, it is not rational.
4. **0.23242526...**: This number does not show a repeating pattern, indicating it is a non-repeating decimal. Non-repeating decimals are irrational numbers. Therefore, this number is also not rational.
From the analysis, the only rational number among the options is **0.98989898...**.
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