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**Properties and Scientific Notation**

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**Try changing these numbers from Scientific Notation to Standard Notation:**

9.678 x 104 x 10-3 x 107 x 10-5 96780

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Convert these: 1.23 X , X 106 6,806,000

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2.48 X 103 2, X 106 6,123, X X

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**Try changing these numbers from Standard Notation to Scientific Notation:**

.08376 5673 x 106 3.45 x 10-5 8.376 x 102 5.673 x 103

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**Using scientific notation, rewrite the following numbers.**

Now You Try Using scientific notation, rewrite the following numbers. 347,000. 3.47 X 105 902,000,000. 9.02 X 108 61,400. 6.14 X 104

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**Commutative Properties**

Changing the order of the numbers in addition or multiplication will not change the result. Commutative Property of Addition states: = or a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

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**Associative Properties**

Changing the grouping of the numbers in addition or multiplication will not change the result. Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ c Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)

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**Distributive Property**

Multiplication distributes over addition.

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**Additive Identity Property**

There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.

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**Multiplicative Identity Property**

There exists a unique number 1 such that the number 1 preserves identities under multiplication. a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

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**Additive Inverse Property**

For each real number a there exists a unique real number –a such that their sum is zero. a + (-a) = 0 In other words opposites add to zero.

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**Multiplicative Inverse Property**

For each real number a there exists a unique real number such that their product is 1.

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