Real Number System

Recall that irrational numbers are non-terminating (do not end) and non-repeating (do not repeat).

If we put $$\sqrt[]{16}$$ in our calculator we find it is 4. This number ends, making it rational (not irrational).

Natural numbers are counting numbers.

Natural numbers are non-decimals, positive and not 0.

Natural numbers are all whole numbers except 0.

$$-\frac{75}{3}=-25$$

All numbers you see this year are real.

-25 ends making it rational.

-25 is not a decimal making it an integer.

-25 is negative so it is NOT whole.

$$1,378,472,706$$

This number ends, so it is rational.

This number is not a decimal, so it is an integer.

This number is positive, so it is whole.

This number is not 0, so it is natural.

$$\pi$$ is a non-terminating (does not end) and non-repeating number (doesn't repeat).

This makes the number irrational.

If you put $$-\ \sqrt[]{13}$$ in your calculator, you will see it does not end (non-terminating) and does not repeat (non-repeating). That makes this irrational.

Just because a number is negative DOES NOT make it an integer.

$$-\ \sqrt[]{100}=-10$$

This number ends, making it rational.

This number is not a decimal, making it an integer.

This number is negative, so it is NOT whole.

The most specific name is Integer. (That is the farthest in circle the number fits in)

We must convert percents to a "regular" number. If we divide by 100 or move the decimal 2 spots left, we get the number 3.

3 ends making it rational.

3 is not a decimal making it an integer.

3 is positive making it whole.

3 is a counting number, making it natural.

The farthest circle in that 3 belongs to is natural.

$$\frac{10}{5}=2$$ , $$\sqrt[]{49}=7$$ , $$\ 0$$ , $$500\%=5$$

All of the numbers are rational (they end).

All of the numbers are integer (they decimals).

All of the numbers are whole (they aren't negative).

0 isn't natural.

That means they all have Whole in common as the subset they ALL belong to.

$$-\ \sqrt[]{64}=-8$$

$$\frac{20}{5}=4$$

$$330\%=3.3$$

$$0$$

Since we have decimal, the most specific subset that ALL the numbers fit into is Rational.

(Remember integers can't be decimals... since 330% is 3.3 we can't go any further).