**Rational and Irrational Numbers**

**Both rational and irrational numbers are real numbers.**

This Venn Diagram shows the relationships between sets of numbers. Notice that rational and irrational numbers are contained in the large blue rectangle representing the set of Real Numbers.

- A
**rational number**is a number that can be expressed as a fraction or ratio.

The numerator and the denominator of the fraction are both integers. - When the fraction is divided out, it becomes a terminating or repeating decimal. (The repeating decimal portion may be one number or a billion numbers.)
- Rational numbers can be ordered on a number line.

**Examples of rational numbers are:**

**Hint:** When given a rational number in decimal form and asked to write it as a fraction, it is often helpful to “say” the decimal out loud using the place values to help form the fraction.

**Examples:** Write each rational number as a fraction:

**Hint:** When checking to see which fraction is larger, change the fractions to decimals by dividing and compare their decimal values.

**Examples:**

An **irrational number** cannot be expressed as a fraction.

- Irrational numbers cannot be represented as terminating or repeating decimals.
- Irrational numbers are non-terminating, non-repeating decimals.
**Examples of irrational numbers are:**

**Note:** Many students think that π is the terminating decimal, 3.14, but it is not. Yes, certain math problems ask you to use π as 3.14, but that problem is rounding the value of to make your calculations easier. π is actually a non-ending decimal and is an irrational number.

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