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Exp3 Scientific Notation (4 operations)
Συνεισφορά από: Cason
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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