4 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.
5 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 = …which can be written as:= 2 ÷ 7 = …which can be written as:= 5 ÷ 6 = …which can be written as:= 3 ÷ 11 = …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.
6 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.
7 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.