![Page 1: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/1.jpg)
Operations with Scientific Notation
![Page 2: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/2.jpg)
Addition and Subtraction Format
Addition(N * 10x) + (M * 10x) = (N + M) * 10x
Subtraction(N * 10y) - (M * 10y) = (N-M) * 10y
![Page 3: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/3.jpg)
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 )
![Page 4: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/4.jpg)
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
![Page 5: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/5.jpg)
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
![Page 6: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/6.jpg)
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
![Page 7: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/7.jpg)
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.
![Page 8: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/8.jpg)
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.
![Page 9: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/9.jpg)
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
![Page 10: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/10.jpg)
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
![Page 11: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/11.jpg)
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
![Page 12: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/12.jpg)
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
![Page 13: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/13.jpg)
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
![Page 14: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/14.jpg)
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
![Page 15: Operations with Scientific Notation. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M](https://reader036.vdocuments.net/reader036/viewer/2022082403/56649ed15503460f94be0d35/html5/thumbnails/15.jpg)
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