1. Select the numbers which are rational numbers. a. 2.2525252525 b. 0.5555555 c. \( \sqrt{2} \) d. 4.97654321 e. \( \sqrt{-100} \)
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Rational numbers are those that can be expressed as a fraction \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \). Numbers a (2.2525252525), b (0.5555555), and d (4.97654321) are all rational because they can be expressed as fractions: \( \frac{225}{99} \), \( \frac{5}{9} \), and \( \frac{497654321}{100000000} \), respectively. On the other hand, \( \sqrt{2} \) is an irrational number since it cannot be expressed as a fraction of two integers, and \( \sqrt{-100} \) is also irrational, as it results in an imaginary number (10i) since the square root of a negative number is not real.