The Real Number Line
Integers
...,-4,-3,-2,-1,0,1,2,3,4,... Most people deal with those numbers on the right side starting with 1. Negative numbers seem difficult for most people to understand since they rarely deal with them. An easy way to think about them as money you owe. -1 represents a debt of 1 dollar & so on. All of these numbers can be represented by a point or dot
on the real number line. However, you must realize that there are gaps between these numbers where other numbers exist. If we travel to the far right on the number line the numbers get larger and conversely, they get smaller as we travel to the left. So, -25 is smaller than -3, while 25 is larger than 3. Tricky. Now, let's take a look at the numbers in the gaps between these whole numbers (integers).
Rational Numbers: Any number that can be expressed as a/b where a and b are integers (whole numbers). So, if b=1, they will be whole numbers since every whole number has a denominator of 1 (which is not written). For example, the number 14 is really 14/1. However, if the denominator is not 1, then we start to fill in the gaps. For example 7/8 is not a whole number. It is close to 1. To see how close your fraction is to a whole number just use a basic calculator and divide the top by the bottom. If you do this with 7/8, you will get 0.875. Moving the decimal two places to the right gives you the percentage 87.5%.
Try to write all mixed numbers as one fraction. That way, you can better get where it is located on the number line. For example, 3&5/8 can be written as 8x3+5 over 8 or 29/8. Doing the division, we get 3.625. This will be just a little pass the midpoint between 3 and 4. Knowing the location of numbers is important. Just remember, on the number line, a number to the right of another number is always larger. So, 3.625 is larger than 3.622 but smaller than 3.630. Special mathematical symbols are used for "greater than" and "less than". a>b means a is greater than b or saying differently, b is less than a, written b < a. So, we can state 3.6 > 3.5 and 7.88 < 7.91.
Irrational Numbers.: Not rational. Numbers like the square root of 2 (two identical numbers that multiply to give you a result of 2) is not rational. It can be approximated by 1.414, however, it goes on indefinitely (never ending & non-repeating). On the other hand, .3333...for ever can be written as 1/3, therefore is a rational number. It turns out that every repeating decimal is a rational number. This is easily proven. There are infinitely many rational and irrational numbers. One very popular irrational number you might have been exposed to is Pi. The circumference of a circle divided by its diameter regardless of the size of the circle.