# Rational and Irrational Numbers

## Rational and Irrational Numbers

### Rational Numbers

Any number that can be expressed in the form where *p*, *q* are integers and *q* 0 is called a rational number. *p* is called the numerator and *q* the denominator of the rational number.

Any integer can be expressed as a rational number. For example, 5 can be written as in the rational form.

The numbers ,,,,,,… are all rational numbers

All fractions are rational numbers. All integers are also rational numbers. There are many rational numbers which are neither fractions nor integers.

Rational numbers can also be represented on the number line.

*Example:* Which of the following is (are) rational number(s)?

2, , , -9,

It can be seen that apart from, all other numbers can be written in the form.

So, except, all the given numbers are rational numbers.

### Irrational Numbers

All numbers which are not rational are called irrational numbers, which means all the numbers that ** cannot** be put in the form where

*p*,

*q*are integers and

*q*0 are called ‘irrational numbers’.

Any rational number will be a terminating decimal or a repeating decimal. For example, = 0.875(terminating decimal)

= 0.41666…(repeating decimal)

An irrational number is a decimal that is neither terminating nor repeating.

The square roots of 2, 3, 5, 6, 7, 8 are all irrational numbers.

*Example:* Which of the following is NOT irrational?

and are irrational numbers.

= 4, which is a rational number.

= = 2, which is also a rational number.

So, and are NOT irrational numbers.

##### Answer key

- Yes
- π
- 0 is a rational number because we can write it as ,, which implies that 0 is a rational number.
- (A)

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__Arithemetic & Pre Algebra__

**The Number System**

1) Rational and Irrational Numbers

2) Compare Irrational Numbers

3) Fractions and Repeating Decimals

4) Approximating Square Roots

__Algebra__

**Expressions and Equations**

1) Exponents and their properties

2) Square roots and Cube roots

3) Scientific Notation – addition, subtraction, division and multiplication

4) Equations with variables on both sides

5) Linear equations with one, zero, or infinite solutions

6) Age Word Problems

7) Solve systems of linear equations with elimination and substitution

8) Word Problems on System of Linear Equations

__Geometry__

1) Parallel Lines

2) Congruent Angles

3) Finding Angle Measures

4) Pythagorean Theorem

5) Distance Formula

6) Word problems on Volume of Cones, Cylinders, and Spheres

__Statistics and Probability__