SPI 2.2 Rational and Irrational Numbers Coach Lesson 2

Question 1

1

What are integers?

Give examples.

Answer 1

Integers are whole numbers and their opposites.

Examples are …-3, -2, -1, 0, 1, 2, 3, ….

Question 2

2

What are rational numbers?

Give examples.

Answer 2

Rational numbers are

1. numbers that can be expressed as integer/integers, where the denominator cannot be zero
2. fractions, mixed numbers, improper fractions, repreating decimals, and terminating decimals
3. the square root of a perfect square

Examples 0.3 repeating, 0.25, -12, 102, 36.2, -23.5.

Question 3

3

What are irrational numbers?

Give examples.

Answer 3

Irrational numbers

• cannot be expressed as integer/integer
• are non-terminating and non-repeating decimals
• square roots of non-perfect squares

Examples are pi, square root of 2, square root of 3, 8.321.456…

Question 4

4

EX1: How do you determine if a number is rational or irrational.

For example, the square root of 149?

Answer 4

Use a calculator to covert the number to a decimal.

• The square root of 149 is 12.20655562…

If the decimal terminates or repeats, the original number is rational.

If the decimal is non-terminating AND non-repeating, the original number is irrational.

• Since 12.20655562… does not terminate and does not repeat, the square root of 149 is irrational.

Question 5

5

EX2: Besides calculating the square root of a number, what is another method to decide if a number is rational or irrational?

• For example, the square root of 169?

Answer 5

Determine if the number is a perfect square or not.

• If a number is a perfect square, its square root will be rational.
• If a number is non a perfect square, its square root will be irrational.
• Since 169 is a perfect square (13 x 13), the square root of 169 is rational.

Question 6

6

If you are given a list of numbers, how do you identify which ones are rational and which are irrational?

Answer 6

1. Convert ALL of the numbers in the list to decimals.
2. Then decide.

Question 7

7

Are all expressions that include pi irrational?

Answer 7

No.

Some rational examples are:

• π/1
• (π + 4)/(4 + π)
• 2π/2π