### Number Sets Worksheets

The number system is divided into several sets. Basically, this includes the set of real and imaginary numbers. These numbers are expressed in the form, $$a+bi$$ where $$a$$ represents the real number and $$bi$$ represents the imaginary number. The field of real numbers is further classified into rational and irrational numbers. Rational numbers are those numbers that can be written as a quotient of any two real numbers, say $$p$$ and $$q$$ except when the denominator, $$q=0$$ while irrational numbers are those numbers that cannot be expressed as a quotient of an integer and a counting number. Rational numbers include fractions, decimals and integers while irrational numbers commonly include the square roots of non–perfect square numbers and the value of $$\pi$$. Shown below is a diagram representing the number sets and some examples per set.

Examples

A. True or False

Based from the diagram, determine whether each statement is true or false.
1. Every irrational number is a real number.
2. $$\sqrt{8}$$ is an irrational number.
3. Every natural number is a whole number.
4. – 2.5 is a negative integer.
5. 10 is a rational number.
6. Every whole number is a counting number.
7. Every irrational number is a real number.
8. Every rational number is a fraction.
9. Every decimal number is rational.
10. $$-\sqrt{16}$$ is imaginary.
1. True
2. True
3. True
4. False
5. True
6. False
7. True
8. False
9. True
10. False
B. Consider the given set of numbers below. Identify the elements for each set.

Given:
$S=\left \{\left{ -2, 5, 0, 2.5, 2\sqrt{7}, \displaystyle \frac{24}{7}, 3\pi, \displaystyle \frac{2}{3}, 0.2\overline{35}, 2\displaystyle \frac{3}{4} \right}\right \}$
1. Rational numbers
2. Natural numbers
3. Integers
4. Whole numbers
5. Counting numbers
6. Negative integers
7. Fractions
8. Irrational numbers
9. Natural numbers
10. Decimal numbers
1. $$-2, 5, 0, 2.5, \displaystyle \frac{24}{3}, \displaystyle \frac{2}{3}, 0.2\overline{35}, 2\displaystyle \frac{3}{4}$$
2. $$5$$
3. $$–2, 5, 0, \displaystyle \frac{24}{3}$$
4. $$0,5$$
5. $$5$$
6. $$–2$$
7. $$\displaystyle \frac{24}{3}, \displaystyle \frac{2}{3}, 2\displaystyle \frac{3}{4}$$
8. $$3\pi, 2\sqrt{7}$$
9. $$5$$
10. $$2.5, 0.2\overline{35}$$