1. Scientific Notation A short-hand way of writing large numbers without
writing all of the zeros.

2. The Distance From the Sun to the Earth
93,000,000

3. Step 1 93,000,000 = 9.3000000 Move decimal left
Leave only one number in front of decimal
93,000,000 =

4. Step 2
Write number without zeros
93,000,000 = 9.3

5. Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal
Make that your power of ten
93,000,000 = 9.3 x 10 7

6. The power of ten is 7 because the decimal moved 7 places. 7
93,000,000 = 9.3 x 10 7

7. 93,000, Standard Form
9.3 x Scientific Notation

8. Practice Problem -----> -----> -----> ----->
Write in scientific notation.
Decide the power of ten.
98,500,000 = 9.85 x 10?
64,100,000,000 = 6.41 x 10?
279,000,000 = 2.79 x 10?
4,200,000 = 4.2 x 10?
9.85 x 107
----->
6.41 x 1010
----->
2.79 x 108
----->
----->
4.2 x 106

9. More Practice Problems
On these, decide where the decimal will be moved.
734,000,000 = ______ x 108
870,000,000,000 = ______x 1011
90,000,000,000 = _____ x 1010
Answers
3) 9 x 1010
7.34 x 108
2) 8.7 x 1011

10. Complete Practice Problems
Write in scientific notation.
50,000
7,200,000
802,000,000,000
Answers
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011

11. Scientific Notation to Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
move the decimal
--->
340,000 in standard form

12. Move the decimal to the right.
Write in Standard Form
Move the decimal to the right.
6.27 x 106
9.01 x 104
6,270,000
90,100

13. Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000

14. Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01
10-3 = 1/1000 = 0.001
10-4 = 1/10000 =

15. Scientific Notation
We use the idea of exponents to make it easier to work with large and small numbers.
10,000 = 1 X 104
250,000 = 2.5 X 105
Count places to the left until there is one number to the left of the decimal point.
230,000 = ?
35,000 = ?

16. Scientific Notation Continued
= 6 X 10-5
= 4.5 X 10-4
Count places to the right until there is one number to the left of the decimal point
0.003 = ?
= ?

17. Multiplying with Scientific Notation
Add the Exponents
102 X 103 = 105
100 X 1000 = 100,000

18. Multiplying with Scientific Notation
(2.3 X 102)(3.3 X 103)
230 X 3300
Multiply the Coefficients
2.3 X 3.3 = 7.59
Add the Exponents
102 X 103 = 105
7.59 X 105
759,000

19. Multiplying with Scientific Notation
(4.6 X 104) X (5.5 X 103) = ?
(3.1 X 103) X (4.2 X 105) = ?

20. Dividing with Scientific Notation
Subtract the Exponents
104/103 = 101
10000X 1000 = 10

21. Dividing with Scientific Notation
(3.3 X 104)/ (2.3 X 102)
33000 / 230 =
Divide the Coefficients
3.3/ 2.3 =
Subtract the Exponents
104 / 102 = 102
X 102

22. Dividing with Scientific Notation
(4.6 X 104) / (5.5 X 103) = ?
(3.1 X 103) / (4.2 X 105) = ?

23. Addition and subtraction Scientific Notation
2.0 x x 103
.2 x x 103
= .2+3 x 103
= 3.2 x 103
1. Make exponents of 10 the same
2. Add and keep the 103 intact
The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same.
2.0 x x 105
2.0 x x 107
= x 107
= x 107
1. Make exponents of 10 the same
2. Subtract and
keep the 107 intact