Repeating Decimals

• Repeating decimals are decimals that contain a infinite number of digits.

• Examples:

0.333…

7.689689…

9.1

Non Repeating Decimals

• Non repeating decimals are decimals that either end or carry on forever in a random way.

• Examples:

0.3297680486…

2.7

Properties of Real Numbers

Commutative Properties

• Commutative Property of Addition

•

• Example:

• Commutative Property

• Commutative Property of Multiplication

•

• Example:

abba abba

3773 3773

Associative Properties

• Associative Property of Addition

•

• Example:

• Associative Property of Multiplication

•

• Example:

)( cbacba

)54(65)46( )54(65)46(

)( cbacba

Distributive Property

• Distributive Property

Example:

Example:

• Distributive Property

acabcba )(

acabcba )(

2545)24(5

2545)24(5

Mrs. de Nobrega’s math class

Mrs. de Nobrega’s math class

Identity Properties

• Identity Property of Addition

Example:

• Identity Property of Multiplication

Example:

aa 0 aa 1

505 616

Inverse Properties

• Inverse Property of Addition (Opposite)

For every a, there is an additive inverse –a such that a + (-a) = 0

Example:

5 + (-5) = 0

• Inverse Property of Multiplication (Reciprocal)

– For every a ( ), there is a multiplicative inverse such that

Example:

0a

11

a

a

15

15

Properties of Real Numbers

• Example – Identifying Properties

– Name the property that each equation illustrates. Explain.

•9 + 7 = 7 + 9

•

• t + 0 = t

• –(q + 3)= -q - 3

)34(3)4( dd

Properties of Real Numbers

• Answers:

– Commutative Property of Addition, because the order of the addends changes.

– Associative Property of Multiplication, because the grouping of the factors changes.

– Identity Property of Addition, because the sum of a number and zero is the number.

– Distributive Property, because you are finding the area.