Rational and Irrational Numbers.notebook
April 24, 2015
Rational & Irrational Numbers
Rational & Irrational Numbers
Definition: is rational because the radicand (number under the radical) is a perfect square A number that can be written as a simple fraction.
(A set of integers and decimals that repeat or terminate.)
If a radicand is not a perfect square, the root is said to be irrational. In order for a number to be rational, you must be able to divide the fraction and have the decimal either terminate or repeat.
Ex: Examples of rational numbers: 0, ­5, 8, 0.44, ­0.23, 9
, ½ Pi
1 Rational or Irrational?
We have learned about Pi in Geometry. It is the ratio of a circle's circumference to its diameter. It is represented by the symbol .
Rational B
Irrational Answer
Answer
A
A
Discuss why this is an approximation at your table. Is this number rational or irrational?
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2 Rational or Irrational?
3 Rational or Irrational?
0.141414....
B
Irrational A
B
Rational B
Answer
Rational Answer
A
Irrational A
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Rational and Irrational Numbers.notebook
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April 24, 2015
5 Rational or Irrational?
1.222...
B
Irrational A
Rational B
Irrational Answer
Rational Answer
A
A
A
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7 Which is a rational number?
6 Rational or Irrational?
A
π
B
B
Irrational C
D
Answer
Rational Answer
A
B
C
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From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
(Problem from )
B
2
C
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D
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If a rational number is not an integer, then the square root of the rational number is irrational.
1/
For example, 3.6 is irrational and is irrational.
2
Provide an example of a non­integer rational number that shows that the conjecture is false.
D
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From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
examples to support the conjecture.
Answer
A
Answer
8 Given the statement: “If x is a rational number, then is irrational." Which value of x makes the statement false?
9 A student made this conjecture and found two 2.25 = 1.5 1/4 = 1/2
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Rational and Irrational Numbers.notebook
April 24, 2015
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