Rational and Irrational Numbers

Rational Numbers

Can be put in fractional form

The decimal form of the number either terminates (ends) or repeats.

Counting numbers, whole numbers, integers and non-integers are all rational.

Rational Numbers

Examples:

Counting numbers {1,2,3,4,5…}

Whole numbers {0,1,2,3,4,5…}

Integers {…-3,-2,-1,0,1,2,3,4,5…}

Non-integers {5.25, 0.6, 0.18181818, -9.261

Repeating Decimal Terminating

decimal

Irrational Numbers

Can NOT be written as a fraction.

The decimal form of the number never terminates and never repeats.

Irrational Numbers

Example:

Pi π 3.141592654……

Does not terminate, does not repeat.

Real Number System

Real Numbers

Rational Numbers Irrational Numbers

Integers Non-Integers

Whole #s Negative Integers

Practice: Rational or Irrational?

Write whether each number is rational or irrational.

1. -23.75 _________

2. 4.750918362… __________

3. ⅝ ____________

4. 1,469,000 ___________

5. ¼ __________

6. √15 ___________

Answers

1. -23.75 Rational

2. 4.750918362… Irrational

3. ⅝ Rational

4. 1,469,000 Rational

5. ¼ Rational

6. √15 Irrational

Write all the numbers that are Rational.

√81 -9 0.25189687…. 3.66 √2

Rational: √81 -9 3.66