1. Scientific Notation

2. Scientific Notation At the conclusion of our time together, you should be able to: 1.Define scientific notation 2.Convert numbers into scientific notation 3.Convert scientific notation to a standard number

3. What is Scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. For very large and very small numbers, scientific notation is more concise.

4. Scientific Notation Consists Of Two Parts: M = A number between 1 and 10 n = A power of 10 M x 10 n

5. Scientific Notation M x 10 n M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10

6. Other Examples: 5.45E+6 5.45 x 10^6

7. Numbers Less Than 1 Will Have A Negative Exponent. A millionth of a second is: 0.000 001 sec 1 x 10 -6 s 1.0E-6 s 1.0 x 10^-6 s

8. To Change Standard Form To Scientific Notation… Place the decimal point so that there is one non- zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

9. Examples Given: 289 800 000 m Use: 2.898 m (moved 8 places) Answer: 2.898 x 10 8 m Easier Way = M term smaller, so make n term larger - 10 0 to 10 8 Given: 0.000 567 m Use: 5.67 m (moved 4 places) Answer: 5.67 x 10 -4 m Easier Way = M term larger, so make n term smaller - 10 0 to 10 -4

10. To Change Scientific Notation To Standard Form… Simply move the decimal point to the right for positive exponent of 10. Simply move the decimal point to the right for positive exponent of 10. Move the decimal point to the left for negative exponent of 10. Move the decimal point to the left for negative exponent of 10. (Use zeros to fill in places.)

11. Example Given: 5.093 x 10 6 m Answer: 5 093 000 m (moved 6 places to the right) Easier Way = 10 6 to 10 0 = n smaller, so make M term larger! Given: 1.976 x 10 -4 m Answer: 0.000 197 6 m (moved 4 places to the left) Easier Way = 10 -4 to 10 0 = n larger, so make M term smaller!

12. Scientific Notation Let’s see if you can: 1.Define scientific notation 2.Convert numbers into scientific notation 3.Convert scientific notation to a standard number

13. Learning Check Express these numbers in Scientific Notation: Express these numbers in Scientific Notation: 1) 405 000 cm 2) 0.003 872 cm 3) 3 000 000 000 cm 4) 2 cm 5) 0.478000 cm cm 4.05 x 10 5 cm cm 3.872 x 10 -3 cm cm 3 x 10 9 cm cm 2 x 10 0 cm cm 4.78000 x 10 -1 cm

14. Scientific Notation Calculations

15. Scientific Notation At the conclusion of our time together, you should be able to: 1.Multiply and divide numbers that are in scientific notation 2.Add and subtract numbers that are in scientific notation

16. Example #16 (3 x 10 2 m)(8 x 10 -4 m) Answer: multiply M terms 24 Add n terms -2 24 x 10 -2 m 2 Adjust to correct scientific notation 2.4 x 10 -1 m 2 Adjust to correct number of sig figs 2 x 10 -1 m 2

17. Example #17 (5.000 x 10 5 m)/(3500 m) Answer: divide M terms 0.001 428 Subtract n terms 5 0.001 428 x 10 5 Adjust to correct scientific notation 1.428 x 10 2 Adjust to correct number of sig figs 1.4 x 10 2

18. Example #18 (5.0 x 10 4 m)(8.230 x 10 6 m) /(1.99 x 10 18 m) Answer: multiply and divide M terms 20.678 m Add and subtract n terms -8 20.678 x 10 -8 m Adjust to correct scientific notation 2.0678 x 10 -7 m Adjust to correct number of sig figs 2.1 x 10 -7 m

19. Example #13 (5.0 x 10 -3 m)-(5.0 x 10 -8 m) Answer: can only subtract like powers Adjust to larger power (5.0 x 10 -3 m)-(0.000050 x 10 -3 m) = 4.999950 x 10 -3 m Adjust to correct number of decimal places 5.0 x 10 -3 m Adjust to correct scientific notation 5.0 x 10 -3 m

20. Example #14 (5.0 x 10 -3 m) + 0.774 m Answer: can only add like powers Adjust to larger power (0.0050 x 10 0 m) + 0.774 m = 0.7790 m Adjust to correct number of decimal places 0.779 m Adjust to correct scientific notation 7.79 x 10 -1 m

21. Example #15 (5.0 x 10 -3 m) + (5.0 x 10 -4 m) - 0.009 38 m Answer: can only add like powers Adjust to larger power (0.0050 x 10 0 m) + (0.000 50 m) – 0.009 38 m -0.003 88 m Adjust to correct number of decimal places -0.003 9 m Adjust to correct scientific notation -3.9 x 10 -3 m

22. Scientific Notation Let’s see if you can: 1.Multiply and divide numbers that are in scientific notation 2.Add and subtract numbers that are in scientific notation