We are learning to identify irrational numbers. Friday, April 21, 2017

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Presentation transcript:

We are learning to identify irrational numbers. Friday, April 21, 2017

What about ? Is there a whole number solution? Why not? Try the square root of 2 on a calculator…write you solution. This is known as an irrational number.

Rational vs. Irrational Numbers

Rational vs. Irrational Numbers Irrational Numbers – A number that when written as a decimal does not end and never repeats. An irrational number can never be written as a fraction. Rational Number – A number that when written as a decimal either stops or repeats in a pattern. All rational numbers can be written as fractions.

Rational vs. Irrational Numbers When a decimal repeats in a pattern you can draw a bar above the repeating part to demonstrate the pattern. = 1 ÷ 3 = 0.33333333333333333…which can be written as: = 2 ÷ 7 = 0.28571428571428571…which can be written as: = 5 ÷ 6 = 0.83333333333333333…which can be written as: = 3 ÷ 11 = 0.2727272727272727…which can be written as: . All of these are examples of RATIONAL NUMBERS because… They are written as fractions and decimals that repeat in a pattern.

Rational vs. Irrational Numbers These are both examples of IRRATIONAL NUMBERS because… When written as a decimal they will never end, and never repeat in a pattern. Also, these numbers cannot be written as a fraction. Every square root of a non-perfect square is an irrational number.

Fix the common mistake: Jim believes that is an irrational number because it can be written as the non-terminating decimal . Why is his thinking incorrect? Write 3 complete sentences that would help Jim fix his mistake.