Graphs of real numbers on the number line and classifying real numbers

To visualize and classify real numbers, we can graph them on a number line and identify their types. For example, consider the following:

In Example 1, let’s graph:

• A) all integers x where x is between −3 and 2, including −3 but excluding 2. Here, x is represented by solid dots at each integer from −3 up to 1.
• B) the same range, but with x as any real number between −3 and 2. For this, we draw a continuous line from −3 to 2, with a solid dot at −3 and an open circle at 2 to indicate exclusion.

In Example 2, we classify different real numbers by type:

• A) 1.2: a rational number
• B) 12.363636…: an irrational number
• C) 0: a whole number, integer, and rational number
• D) 5/3​: a rational number.