Real Numbers

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Real Numbers

• Presented by Katie Holmes

Begin the fun!
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What youll learn about

• Irrational numbers
• Rational numbers
• Integers
• Whole numbers
• Natural numbers

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The Real Numbers

• Natural Numbers - The counting numbers starting
  with 1.
• Ex. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10...
• Whole Numbers - The Natural numbers and 0.
• Ex. 0, 1, 2, 3, 4, 5, 6, 7, 8
• Integers The whole numbers and the negatives of
  the natural numbers. Integers are basically the
  entire number line, excluding most fractions and
  decimals.
• Ex. -3, -2, -1, 0, 1, 2, 3
• Fractions that can be reduced down to whole
  numbers (Ex. 8/4) or a negative or a natural
  number (Ex. -10/2) are also integers

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The Real Numbers continued

• Rational Numbers All Integers, Whole numbers,
  and Natural numbers. Rational numbers also
  include terminating decimals (decimals that end),
  and repeating decimals.
• Ex. -2, -1, 0, .5, 1, 1.8, 2
• Irrational Numbers All non-terminating decimals
  (decimals that never end) and non-repeating
  decimals. Any number that is not a perfect square
  has an irrational square root.
• Ex. Pi (3.14.), square root of 2

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Diagram

• All Rational numbers are integers, whole numbers,
  and natural numbers.
• All integers are whole numbers and natural
  numbers.
• All whole numbers are natural numbers.
• Natural numbers are just natural numbers.

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Practice 1

• Any integer is a rational number.

True
False
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Correct!

• Congrats you got that extremely hard question
  right!
• Answer True
• Why Any integer can be formatted as a fraction
  by putting it over 1.

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Practice 2

• Any rational number is an integer.

False
True
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Correct!

• Congrats you got another really difficult
  question correct!
• Answer False
• Why 4/1 can be an integer, but 2/3 (which is a
  rational number) cant be an integer

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Practice 3

• Which number type or types would the following
  number be
• .45

A
B
Natural, Real
Natural, Whole, Real
C
D
Integer, Whole, Rational
Rational, Real
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Correct!

• Yet another correct question! You must be
  cheating.
• Answer B. Rational, Real
• Why This is a terminating decimal, so it can be
  written as a fraction. Since this fraction cannot
  be reduced to a whole number, it is not an
  integer or a natural number. Since all rational
  numbers are real numbers, it is also a real
  number.

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Practice 4

• What would the following number be considered?
• 10

A
B
Irrational
Natural, Real, Whole, Integer, Rational
C
D
The number of fingers I have!
Natural, Real, Irrational, Whole, Integer
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Correct!

• I really think you are cheating.
• This is just too hard for you to solve on your
  own.
• Answer B. Natural, Real, Whole, Integer,
  Rational
• Why 10 is a counting number. It falls into all
  number categories except irrational. It is also
  the number of fingers you have, but if you chose
  that answer I truly wonder why youre in this
  class.

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Practice 5

• Which number type or types would the following
  number be
• -9/3

A
B
Rational, Real
Integer, Rational, Whole
D
C
Integer, Rational, Unreal
Integer, Real, Rational
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Correct!

• I bet youre sick of this Power Point by now.
• Answer D. Integer, Real, Rational
• Why This is a fraction, BUT it reduces down to
  -3, so that would make it an integer.

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Practice 6

• Which number type or types would the following
  number be
• 3.14159265

B
A
Real, Rational, Whole, Irrational
Real, Rational
C
D
Real, Rational, Integer
Irrational, Real
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Correct!

• Wow, what a surprise.
• You got yet another one right.
• Answer D. Irrational, Real
• Why This number is pi. Pi is NOT a repeating
  decimal or a terminating decimal. Therefore, it
  is considered to be Irrational.

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Practice 7

• Put the following numbers in order from least to
  greatest
• 3, 2.5, -32, 8/3, 6/4

A
B
3, 2.5, -32, 8/3, 6/4
6/4, -32, 8/3, 2.5, 3
C
D
-32, 6/4, 2.5, 8/3, 3
-32, 8/3, 2.5, 6/4, 3
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Correct!

• So, did you get the answer right on the first
  try? I hope so.
• Answer 6/4, -32, 8/3, 2.5, 3
• Why Because.

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Ok, get ready for this.This question is the
hardest of them all.I hope you read the notes
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Practice 8

• Did you have fun doing your power point?

Yes
No
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Congratulations!!

• You have made it through my excruciatingly easy
  Power Point without falling asleep!
• Give yourself a pat on the back!

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My Wonderful Resources

• http//www.purplemath.com/modules/numtypes.htm
• Notes Real Numbers