Answers:
4.27 is rational
0.232342345... is irrational
-13/1 is rational
Explanations:
The fact that 4.27 is a terminating decimal means that we have a rational number. All terminating decimals can be written in a fraction of two integers (positive or negative whole numbers). The word "terminate" means "stop", so the decimal values stop at some point. Note: 4.27 = 427/100 is one way to show that 4.27 is rational
The second value 0.232342345... doesn't seem to have a clear repeating pattern. It's impossible to know what the next value will be. So because of this, the number is irrational. We cannot write it as a fraction of two whole numbers. Other examples of irrational numbers are things like pi = 3.1415... or sqrt(2) = 1.414...
The value -13/1 is rational imply because it is a fraction or ratio of two whole numbers -13 and 1. All fractions like 1/2 or 2/3 or 5/7 are rational numbers. All integers are rational. Note: the denominator can never be zero.
