Operations with Scientific Notation

Addition and Subtraction Format

Addition(N * 10x) + (M * 10x) = (N + M) * 10x

Subtraction(N * 10y) - (M * 10y) = (N-M) * 10y

Different Scenarios•When we add or subtract using scientific

notation, we encounter two scenarios:

1. Same power of tenEx. (3 x 103) + (5 x 103 )

2. Different powers of tenEx. (2 x 104) – (8.3 x 106 )

Same Power of Ten•When we have the same power of ten1. Add/subtract the bases2. Attach the power of ten

2.56 x 103 + 6.964 x 103

Add the Bases: 2.56 + 6.964 = 9.524Attach the power of ten: 9.524 x 103

Same Powers of TenExample: Subtraction

9.49 x 105 – 4.863 x 105

Subtract bases: 9.49 – 4.863 = 4.627Attach power of ten: 4.627 x 105

You Try!•9.0979 x 103 - 3.252 x 103  =  

•6.95 x 104 - 9.94 x 104  =

•3.261 x 107 + 8.294 x 107  =  

•3.262 x 105 + 2.892 x 105  =

5.8459 x 103

-2.99 x 104

11.555 x 107 = 1.1555 x 108

6.154 x 105

Different Powers of Ten•We must have the same power of ten in

order to add or subtract!

•If the powers are different, you must move the decimal either right or left (on one of the numbers) so that they will have the same exponent.

Moving the Decimal•For each move of the decimal to the right

you have to add -1 to the exponent.

•For each move of the decimal to the left you have to add +1 to the exponent.

Different Powers of Ten

2.46 x 106 + 3.476 x 103

If I want to make 103 into 106 I have to shift the decimal 3 places to the left.

(add 3 to the exponent)0.003476 x 103+3

2.46 x 106 + 0.003476 x 106

Answer: 2.463 x 106

Different Powers of Ten

5.762 x 103 – 2.65 x 10-1

If we want to turn 10-1 into 103 we have to move the decimal 4 places to the left

(add 4 to the exponent)0.000265 x 10(-1+4)

5.762 x 103-0.000265 x103

Answer: 5.762 x 103

You Try!•2.3545 x 101 + 3.602 x 102  = 

•3.9261 x 102 + 1.5238 x 103  =  

•3.2641 x 101 + 8.2294 x 104  =  

•3.2005 x 102 - 4.527 x 101  =  

3.8375 x 102

1.9164 x 103

8.2327 x 104

2.7478 x 102

Rounding With Scientific Notation•When we write scientific notation, we

often round to the nearest hundredth.Ex. 3.4563 x 106 3.46 x 106

•When we convert a rounded number to standard form, all of the digits after the ones we are given are written as zero.

Ex. 3.4563 x 106 = 3,456,300 3.46 x 106 = 3,460,000

You Try!•Round to the nearest hundredth, then

convert to standard form.

•1.9164 x 107

•8.2671 x 1012

•5.8456 x 10-2

Multiplication and Division•To multiply or divide, we use our laws of

exponents!

Multiplication:1. Multiply the bases2. Add the powers of ten

Division:3. Divide the bases4. Subtract the exponents

Examples(2.36 x 102 ) * (3.564 x 103 )

2.36 * 3.564 = 8.411042 +3 = 5

8.41104 x 105 8.41 x 105

(12.36 x 102 ) ÷ (3.563 x 103 )12.36 ÷ 3.563 = 3.468986809

2 - 3 = -13.468986809 x 10-1 3.47 x 10-1