1. Properties and Scientific Notation

2. Try changing these numbers from Scientific Notation to Standard Notation:
9.678 x 104
x 10-3
x 107
x 10-5
96780

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

4. 2.48 X 103 2, X 106 6,123, X X

5. 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

6. 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

7. 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.

8. 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)

9. Distributive Property
Multiplication distributes over addition.

10. 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.

11. 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.

12. 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.

13. Multiplicative Inverse Property
For each real number a there exists a unique real number such that their product is 1.