1. Scientific Notation

2. Scientific Notation
Some scientific measurements can result in very large or very small numbers
These numbers can be converted into SCIENTIFIC NOTATION to express them in a more concise form.
EX = x 108 km

3. Why use scientific notation?
To express very large or very small numbers in a more concise form.
Numbers expressed in scientific notation are easier to use in calculations.

4. Scientific notation consists of two parts:
A number between 1 and 10
A power of 10
N x 10x

5. Writing Scientific Notation
In the original number (149,600,000), place the decimal point so that there is one non-zero digit to the LEFT of the decimal point.
N =
Count the number of places that the decimal point “moved” – this will be the exponent
x = 8
1.496 x 108 km

6. Scientific Notation of Small Numbers
In small numbers, the decimal place will be moved to the RIGHT
N = 5.67
The exponent will then be NEGATIVE:
5.67 X 10-4

7. Your Turn Express 289,800,000 in proper scientific notation
Which way will you move the decimal?
How many places will you move the decimal?

8. Answer You would move the decimal 8 places to the left
Answer: x 108

9. Your Turn Express 0.000567 in proper scientific notation
Which way will you move the decimal?
How many places will you move the decimal?

10. Answer You would move the decimal 4 places to the right
Answer: 5.67 x 10-4

11. To change scientific notation to standard form…
Simply move the decimal point to the right for positive exponent 10.
4.56 x 104 = 45,600
Move the decimal point to the left for negative exponent 10.
4.56 x 10-4 =
(Use zeros to fill in places.)

12. Your Turn Express 5.093 x 106 in standard form
Which way will you move the decimal?
How many places will you move the decimal?

13. Answer You would move the decimal 6 places to the right

14. Your Turn Express 1.976 x 10-4 in standard form
Which way will you move the decimal?
How many places will you move the decimal?

15. Answer You would move the decimal 4 places to the left

16. Scientific notation in unit conversions
Scientists also use scientific notation when performing unit conversions

17. Your Turn Express 0.004 mm in meters and scientific notation
Which way will you move the decimal?
How many places will you move the decimal?
Hint: first put the number in correct scientific notation then add the conversion power
mm = 10-3 m

18. Answer You would move the decimal 6 places to the left
Answer: 4.0 x 10-6 m

19. Your Turn Express 5.3 mm in meters and scientific notation
Which way will you move the decimal?
How many places will you move the decimal?
Hint: mm = 10-3 m

20. Answer You would move the decimal 3 places to the left
Answer: 5.3 x 10-3 m