1. Irrational Numbers

3. Irrational Number √2 ∏ (Pi or 3.14)
A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written as a decimal, an irrational number would have an infinite number of digits to the right of the decimal point without repetition.
∏ (Pi or 3.14) √2

5. Decimal Numbers Terminating Rational Repeating Rational
¼ = .25
Repeating Rational
100/3 = = 33.3
19/27 = = 0.703
Non-repeating Irrational
∏= …

6. Rational or Irrational?
3.25 √5
√16
100/3
13.33
Repeating Decimal
10∏

7. Approximate
√36 = 6
√49 = 7 7 6 5 4 3 2 1
√38

8. Compare
√36 = 6
√49 = 7 7 6 5 4 3 2 1
√38
√38 > 6
√38 < 14/2

9. Approximate Irrational Numbers to 2 digit decimal
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√20
4 < √20 < 5
4.52 = 20.25
4.252 = 18.06
4.452 = 19.80
4.482 = 20.07
4.472 = 19.98
4.472 = 19.98

10. Approximate Irrational Numbers to 2 digit decimal
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√52
7 < √52 < 8
7.52 = 56.25
7.252 = 52.56
7.202 = 51.84
7.222 = 52.13
7.212 = 51.98
7.212 = 51.98

11. Approximate Irrational Numbers to 2 digit decimal
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10 √6
2 < √6 < 3
2.52 = 6.25
2.252 = 5.06
2.402 = 5.76
2.452 = 6.00

12. Irrational Review Rational Irrational Fraction Terminating decimal
Repeating decimal
Perfect square
Irrational
Decimal that never repeats (Pi aka π)
Not a perfect square