Irrational numbers never end and they never repeat. They can never be written as a fraction. An example of an irrational number is pi.
Rational numbers can be written as fractions; when written as decimals they either end or repeat in a pattern. An example of a rational number is 9.
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Let's start on the left box:
[tex] \sqrt{16} [/tex] = 4, so it is rational.
1/2 is a fraction, so it is rational.
.[tex] \overline {5} [/tex] is repeating, so it is rational.
-10 is a whole number, so it is rational.
5 is a whole number, so it is rational.
[tex] \sqrt{18} [/tex] = 4.24264... so it is NOT rational.
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Moving on to the right box:
[tex] \sqrt{20} [/tex] = 4.4721... so it is irrational.
3 1/4 is a fraction, so it is NOT irrational.
.12345... is never ending and unrepeating, so it is irrational.
25 is a whole number, so it is NOT irrational.
5.55555... is repeating, so it is NOT irrational.
[tex] \sqrt{1} [/tex] = 1, so it is NOT irrational.
