Exp3 Scientific Notation (4 operations)
To add or subtract numbers in scientific notation,the bases MUST match.  
If the bases already match, just add or subtract the coefficients to the same base.
3 x 103 + 4 x 103 = (3 + 4) x 103 = 7 x 103
Bases - they must match in addition or subtraction.
Adjust 2 x 103 to .2 x 104.  Remember:  When one partof the number is adjusted to make the number larger(as in 103 becoming 104, the other part must be adjusted the other way.  Add coefficients of the samebase.0.2 x 104 + 4 x 104 =           x 104
If adding or subtracting & the bases do not match, first adjust the bases of all numbers to match the larger base.  This lines up the decimals.
2 x 103 + 4 x 104
bases
Make sure the final answer is in scientific notation.
0.3 x 104 + 2 x 104 = 2.3 x 104
In order to add 3 x 103 + 2 x 104, adjust3 x 103 by making the exponent larger and the 3 smaller by one place value each.
3 x 103 becomes 0.3 x 10
+0.34 x 105
5.2 x 105 + 3.4 x 104
5.2   x 105 
 x 105 
+0.72 x 106
9.2 x 106 + 7.2 x 105
9.2   x 106 
 x 106 
 10.52 x 106 
+0.72 x 106
9.8 x 106 + 7.2 x 105
9.8   x 106 
 x 107 
Adjust answer to
scientific notation.
8.3 x 106 + 3 x 104
 x 10
8.3 x 106 - 3 x 104
 x 10
9.8 x 106 - 7.2 x 105
 x 106 
9.8 x 106 - 9.2 x 106
 x 105 
8.5 x 106 - 5 x 104
 x 10
7 x 106 - 5.2 x 104
 x 10
7 x 106 + 5.2 x 104
 x 10
Commutative Property allows us to move numbers aroundwhen a problem is all multiplication.  So change as follows:(2 x 4) • 10(3+4).  Make sure the final answer is inscientific notation.

If multiplying, decimals DO NOT need to line up;therefore, multiply coefficients.  Remember whenmultiplying like based exponents, add the exponents.
2 x 103 • 4 x 104 =            x 107
2 x 103 • 4 x 104
2 x 10  • 4 x 10   =
8 x 10
2

6

6 x 10  • 4 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10
2

6

3.2 x 10  • 4 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10

7

-2

9.5 x 10  • 6 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10

-3

6

2.4 x 10  • 4.8 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10

5

-2

2.4 x 10  • 4.8 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10

-5

-2

Change as follows:(4 ÷ 2) • 10(7-4).  Make sure the final answer is inscientific notation.

If dividing, decimals DO NOT need to line up;therefore, divide coefficients.  Remember whendividing like based exponents, subtract the exponents.
4 x 107 ÷ 2 x 104 =            x 103
4 x 107 ÷  2 x 104
Change as follows:(2 ÷ 4) • 10(7-4)  
Make sure the final answer is in scientific notation.
If dividing, decimals DO NOT need to line up;therefore, divide coefficients.  Remember whendividing like based exponents, subtract the exponents.
2 x 107 ÷ 4 x 104 =            x 102
2 x 107 ÷  4 x 104
= .5 x 103
4.8 x 10  ÷ 2.4 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10

5

2

2.4 x 10  ÷ 4.8 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10

-5

-2

4.8 x 10  • 2.4 x 10   =

Remember:  Your final answer MUST be in

scientific notation.

 x 10

5

-2

Division may also look like this.

4.8 x 10

2.4 x 10

 

Remember:  Your final answer MUST be in

scientific notation.

 x 10

-2

-5

3.2 x 10

6.4 x 10

 

Remember:  Your final answer MUST be in

scientific notation.

 x 10

3

-4

6.4 x 10

3.2 x 10

 

Remember:  Your final answer MUST be in

scientific notation.

 x 10

3

-4

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