Question

1.
Explain the difference between a rational and an irrational number and give an example of each in your explanation.

Answer 1

A rational number is part of a whole expressed as a fraction, decimal or a percentage.

A number is rational if we can write it as a fraction where the top number of the fraction and bottom number are both whole numbers.

The term rational is derived from the word 'ratio' because the rational numbers are figures which can be written in the ratio form.

Every whole number, including negative numbers and zero, is a rational number. This is because every whole number ‘n’ can be written in the form n/1

For example, 3 = 3/1 and therefore 3 is a rational number.

Hope this helps!! ;))
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Answer 2

Rational numbers are numbers that can be written as a fraction. Note that another name for fraction is ratio which is the root of the word Rational. Almost all of the numbers you can think of are rational. All integers, all terminating decimal numbers, and all repeating decimal numbers name a few..
Examples: -4, 3.5, $\frac{3}{8}$

Now you may have already guessed Irrational numbers are numbers that we cannot write as a ratio(fraction). Fortunately, this is a much smaller pool of numbers.. Basically, these are non-terminating and non-repeating decimal numbers.. In other words, decimal numbers that go on forever without ending and never repeating or displaying a pattern.

Where do these types of decimal numbers come from? I would suggest you consider the following two possibilities for now:
1. the number $\pi$
2. anytime you have a non perfect square number under the square root symbol.... i.e. $\sqrt{10}$ Now this is also true for any other radical numbers with different indices.