Rational numbers can be written as fractions or terminating decimals, while irrational numbers are non-repeating and non-terminating decimals that cannot be expressed as fractions. The document provides examples of rational numbers like 3/1, 3/2, 1/9, 4, and 7/1000. Examples of irrational numbers given include the square root of 2 and pi, which have non-repeating decimals. The document includes interactive exercises asking the user to identify numbers as rational or irrational.

1. Classifying Numbers
Rational Numbers vs.
Irrational Numbers

2. A Rational Number: An Irrational Number:
• Cannot be written as a
simple fraction
• Non-terminating decimal
(doesn’t end)
• Non-repeating decimal
(doesn’t repeat in a pattern)
Irrational doesn’t
mean that it’s crazy!
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3. Examples of Rational
Numbers
Click on each number to see explanation
Can be
Can be Can be written as
written as written as 7/1000
3/1 3/2
Repeating
Already in
decimal. Can
fraction form
be written as Can be
1/9 written as 4
and as 4/1
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4. Examples of Irrational
Numbers
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5. More Irrational Numbers
Click on each number to see explanation
Remember . . .
Irrational numbers are non-repeating and non-terminating
decimals and cannot be written as a fraction.
Non-repeating
decimal. Can’t
be written as a
fraction
Non-repeating
decimal. Can’t
be written as
fraction
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6. Try this . . .
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7. Time to practice
INCORRECT
0.5 can be written as
½ and so it is
rational. Try again!
Correct!
0.5 can be written
as ½
Good work!
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8. Time to practice
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9. Time to practice
CORRECT!
-5.060715…
non-repeating, non-
terminating decimal
Good job!
INCORRECT
-5.060715… appears
to be a non-
repeating, non-
terminating decimal
Try again!
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10. Time to practice
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11. Time to practice
INCORRECT
2/3 is a fraction and
so it is rational.
Try again!
CORRECT
2/3 is a fraction.
Good work!
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12. Time to practice
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13. How many RATIONAL
numbers can you find?
Find the answer on the next slide
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14. Did you find
6 rational numbers?
They are:
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