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Classifying Numbers What type of number is that? Classifying Numbers What type of number is that?

Classifying Numbers What type of number is that? - PowerPoint Presentation

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Classifying Numbers What type of number is that? - PPT Presentation

3 ½ ½ 345 123456 Mixed Number Fraction Terminating Decimal Repeating Decimal NonTerminating or NonRepeating Real Numbers The set of real numbers is all numbers that can be written on a number line It consists of the set of rational numbers and the set of ID: 753983

number numbers irrational rational numbers number rational irrational real expressed square integers set repeating school ratio natural fraction examples

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Presentation Transcript

Slide1

Classifying NumbersSlide2

What type of number is that?

3 ½

½

3.45123.456…

Mixed NumberFractionTerminating DecimalRepeating DecimalNon-Terminating or Non-RepeatingSlide3

Real Numbers

The set of

real numbers

is all numbers that can be written on a number line. It consists of the set of rational numbers and the set of irrational numbers.Slide4

A Little Hard to Find History

The history of irrational numbers begins with a discovery by the Pythagorean School in ancient Greece. A member of the school discovered that the diagonal of a unit square could not be expressed as the ratio of any two whole numbers. The motto of the school was “All is Number” (by which they meant whole numbers). Pythagoras believed in the absoluteness of whole numbers and could not accept the discovery. The

member

of the group that made

it was Hippasus and he was

sentenced

to death by drowning.Slide5

Rational Numbers

Rational Numbers

A rational number is any number that can be expressed as

a fraction

or ratio of two numbers .

All

terminating

and

repeating

decimals can be expressed in this way so they are rational numbers.

Examples

a

b

4

5

2

2

3

=

8

3

-3

=

3

1

-

2.7

=

27

10

34.56

=

3456

100

0.3

=

1

3Slide6

Irrational Numbers

Irrational Numbers

An irrational number is any number that

cannot

be expressed as a fraction or a ratio of two numbers. It can only be written as a decimal that goes on forever without repeating.Examples

12.596836…Slide7

Integers

Integers

Integers is defined as all whole numbers both positive and negative, including 0.

-3, -2, -1, 0, 1, 2, 3, 4…Slide8

Whole Numbers

Whole Numbers

Whole numbers are defined as all POSITIVE numbers without a fractional or decimal value AND 0.

0, 1, 2, 3, 4, 5, 6, 7…Slide9

Natural Numbers

Natural Numbers

Natural numbers are all POSITIVE WHOLE numbers starting from 1. Think of when you first learn to count to 10…

1, 2, 3, 4, 5, 6, 7, 8…Slide10

Can a number NOT be real?

There are potential situations that can produce numbers that are NOT real. Here are several examples to help you understand.

Question

What is the square root of -1?Answer: There is NO square root to -1 because there is no number that can be multiplied to itself to produce that product.

QuestionWhat is 5 divided by 0?Answer: There is no solution to this problem. Zero cannot be in the denominator position of a fraction.Slide11

Number

Classification

10

-3

-3 ½

1.235…Slide12

Your Turn

Determine how to classify the following

numbers:

10-3-3 ½1.235…

Real, Rational, Integer, Whole, NaturalReal, Rational, IntegerReal, RationalReal, Irrational