1. 8/27/15
Please complete the “conclusion” questions on the back of your scavenger hunt.
Share with a neighbor.
Let’s share out.

2. Making Sense of Rational and Irrational Numbers
Essential Question: How are rational and irrational numbers simplified?

3. Numbers can also be classified!
Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko!
Animal
Reptile
Lizard
Gecko
Numbers can also be classified!

4. It consists of 2 subsets – rational numbers and irrational numbers.
The set of real numbers is all numbers that can be written on a number line.
It consists of 2 subsets –
rational numbers and irrational numbers.
Irrational numbers
Rational numbers
Real Numbers
Integers
Whole
numbers

5. Rational Numbers Natural Numbers - Natural counting numbers.
1, 2, 3, 4 …
Whole Numbers -
Natural counting numbers and zero.
0, 1, 2, 3 …
Integers -
Whole numbers and their opposites.
… -3, -2, -1, 0, 1, 2, 3 …
Rational Numbers -
Integers, fractions, and decimals.
Ex:
-0.76, -6/13, 0.08, 2/3

6. Name all the sets of numbers to which the given
number belongs. Circle the most specific set.
Integer
, Rational
Rational
Naturals
, Whole
, Integer
, Rational
Whole
, Integer
, Rational
Rational

7. Venn Diagram
Real Numbers
Rational
Integer
Whole
Natural

8. Remember…
Rational numbers can be written as a fraction
or…
as either a terminating or repeating decimal.
4 5 23
3 = 3.8
= 0.6
1.44 = 1.2

9. Classify the Following:
Irrational …
Rational (equals -⅓)

10. Classify the Following:…
Irrational (no end, no repetition) 1⅔
Rational (can be 5/3 )
Rational (equals 10 or 10/1 )

11. Rational v. Irrational – How alike?
Subsets of Real numbers
Can be negative
Can be non-terminating (never end)

12. Rational v. Irrational – How different?
CAN be a fraction
HAS a perfect square root
Can be terminating or repeating decimals
Irrational:
CANNOT be a fraction
Has NO perfect square root
Can only be non-terminating, non-repeating decimals

13. Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as a fraction.
If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so is irrational.
A repeating decimal may not appear to repeat on a calculator, because calculators show a limited number of digits!
Caution!

14. Identify each root as rational or irrational.

15. Decimal to Fraction: A skill you need for this unit!
To change a decimal to a fraction, take the place value and simplify!
0.5 means “5 tenths,” so start with 5/10
Now simplify 5/10 to ½
So… 0.5 = ½

16. Converting Fractions and Decimals
To change a fraction to a decimal, take the top divided by the bottom, or numerator divided by the denominator.

17. Complete the table.
Fraction
Decimal

18. Repeating Decimals
Fraction
Decimal
Every rational number (fraction) either terminates
OR repeats when written as a decimal.

19. Repeating Decimals
Fraction
Decimal

20. Repeating Decimals
Fraction
Decimal

21. Rational Numbers CAN be made into a fraction a/b, where b ≠ 0.
A repeating OR terminating decimal.
2/3 …

22. Irrational Numbers CANNOT be made into a fraction a/b, where b ≠ 0.
A non-repeating AND non-terminating decimal number. π …