Properties and Scientific Notation

Try changing these numbers from Scientific Notation to Standard Notation:

1) 9.678 x 104

2) 7.4521 x 10-3

3) 8.513904567 x 107

4) 4.09748 x 10-5

96780

.0074521

85139045.67

.0000409748

Convert these:

1.23 X 105

123,0006.806 X 106

6,806,000

2.48 X 103

2,480

6.123 X 106 6,123,0

1.248 X 10-6

.000001248

6.123 X 10-5

.00006123 00

Try changing these numbers from Standard Notation to Scientific Notation:

1) 9872432

2) .0000345

3) .08376

4) 5673

9.872432 x 106

3.45 x 10-5

8.376 x 102

5.673 x 103

Now You TryUsing 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

Commutative Properties

• Changing the order of the numbers in addition or multiplication will not change the result.

• Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a.

• Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

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)

Distributive Property

• Multiplication distributes over addition.

acabcba

5323523

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.

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.

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.

Multiplicative Inverse Property

• For each real number a there exists a unique

real number such that their product is 1. 1

a

11

a

a