To determine which number is rational, we first need to remember that a rational number is any number that can be expressed as the quotient of two integers (where the denominator is not zero) or as a terminating or repeating decimal.
Let's analyze each option:
-
15−−√ (square root of 15): This number is irrational because the square root of a non-perfect square is not a fraction.
-
0.98989898…: This is a repeating decimal (0.98 repeated), which can be expressed as a fraction (specifically, \(\frac{98}{99}\)). Thus, it is a rational number.
-
0.23242526…: This number does not exhibit a repeating pattern and appears to be a non-repeating decimal, making it irrational.
-
2√/4: This can be simplified to \(\frac{2\sqrt{2}}{4} = \frac{\sqrt{2}}{2}\). The square root of 2 is irrational, so this is also irrational.
Based on this analysis, the rational number from the options given is:
0.98989898…
1 answer