Transcript 1.3 - Exploring Real Numbers

1.3 Exploring Real
Numbers

Real Numbers:
◦ The set of numbers containing both rational and irrational
numbers
◦ All the numbers we deal with are REAL 
*All numbers are either Rational or Irrational*

Rational Numbers:

Irrational Numbers:
◦ Any number you can write as a fraction
◦ Any decimal that either ends or repeats with a pattern
◦
◦
◦
◦
Any number that cannot be written as a fraction
Non-terminating, non-repeating wacky decimals
Examples?
If a number is irrational, it cannot belong to any other set
Vocabulary

If a number is rational, it could also be one of
the following:

Natural Numbers:

Whole Numbers:

Integers:
◦ 1,2,3,4….
◦ Also called Counting Numbers - These are the numbers
we naturally count with
◦ 0,1,2,3….
◦ Only positive numbers and 0 (the word “whole” has an 0
in the middle!)
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◦
◦
◦
Negatives and positive numbers and 0
No fractions or decimals
All the numbers you see on my number line
-2, -1, 0, 1, 2…
More Vocabulary…

a) -13
◦ Rational numbers
◦ Integers
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b) 3.28
◦ Rational numbers
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c)
Rational numbers
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d) 42
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◦
◦
◦
Rational numbers
Natural numbers
Whole Numbers
Integers
1. Identifying Sets of Numbers

a) outdoor temperatures
◦ Integers or Rational Numbers
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b) the number of beans in a bag
◦ Whole Numbers
◦ Why not Natural Numbers?
2. Identifying Sets of Numbers
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A counterexample is an example that
proves a statement false.

True or False: All negative numbers are
integers.
◦ False
◦ Counterexample?
3. Counterexamples

Inequality: compares the value of two
quantities, using <, >, ≤, or ≥.

Compare the following fractions:
4
4
18
24/7
13
15
4. Inequalities
7

Write - , - , and to greatest.
in order from least
◦ Find the decimal approximation of each.
◦- ,- ,-
5. Order fractions
Opposites are on opposites sides of zero
and are the same distance away from
zero.
 Examples?

◦ -2 and 2, -6 and 6, etc.
Absolute Value is the distance a number
is from zero.
 a) l-2.5l
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◦ 2.5
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b) l7l
◦7
4. Opposites and Absolute Value
 Keep
your assignment out.
 We are going to grade.
 Please bring a pen to class to
use.
 Remember, no stars, just a
mark if the answer is wrong.
Wednesday, August 24
1.
2.
3.
4.
5.
6.
7.
8.
Integers, rational
Rational
Rational
Natural, whole,
integers, rational
Rational
Integers, rational
Whole, integers,
rational
Rational
Rational
10. Irrational
11. Answers vary
12. Answers vary
13. Answers vary
14. Rational
15. Whole
16. Integers
17. Whole
18. Rational
9.
Answers for 1-18
20. False
22. True
24. >
26. >
28. 2.001, 2.01,
2.1
30. -5/6, -1/2,
2/3
32. 0.63, 0.636,
7/11
34. 4
36. 9/14
38. 3/5
40. 1295
Answers for 20-40 even