1. SCIENTIFIC NOTATION (and Calculators) Convert 276Gl → pl 276Gl = 276000000000000000000000pl Convert 146ng → Mg 146ng = 0.000000000000146Mg

2. Q: Is it convenient to use these types of numbers? A: NO!!!!!!  Scientific Notation is used to represent these very large/small numbers.

3. Rules for Scientific Notation The numerical part of the quantity is written as a number between 1 and 10 multiplied by a whole-number power of 10. M = 10 n where: 1 ≤ M < 10 n is an integer n is an integer

4. If the decimal point must be moved to the right to achieve 1 ≤ M < 10, then n is negative (-). If the decimal point must be moved to the left to achieve 1 ≤ M < 10, then n is positive (+). 10 0 = 1

5. Therefore written in proper scientific notation: 276000000000000000000000 pl = 2.76 x 10 23 pl 0.000000000000146ng = 1.46 x 10 -13 Mg

6. Calculator Buttons In class examples of E, EE, and positive/negative exponents.

7. Addition & Subtraction If the numbers have the same exponent, n, add or subtract the values of M and keep the same n. 3.7 x 10 4 + 6.2 x 10 4 = (3.7 + 6.2) x 10 4 = 9.9 x 10 4

8. Example-2 9.3 x 10 7 - 4.1 x 10 7 = (9.3 – 4.1) x 10 7 = 5.2 x 10 7

9. If the exponents are not the same, move the decimal point to the left or right until the exponents are the same. Then add or subtract M. Example-1 2.1 x 10 8 + 7.9 x 10 5 = 2.1 x 10 8 + 0.0079 x 10 8 = (2.1 + 0.0079) x 10 8 = 2.1079 x 10 8 or

10. Example – 2 2.1 x 10 8 + 7.9 x 10 5 = 2100 x 10 5 + 7.9 x 10 5 = (2100 + 7.9) x 10 5 = 2107.9 x 10 5 = 2.1079 x 10 8 Exactly the same as previous example

11. If the magnitude of one number is very small compared to the other number, its effect on the larger number is insignificant. The smaller number can be treated as zero. (9.99 x 10 3 = 9999) 7.98 x 10 12 - 9.99 x 10 3 = 7980000000 x 10 3 - 9.99 x 10 3 = (7980000000 - 9.99) x 10 3 = 7979999990.01 x 10 3 = 7.98 x 10 12

12. Multiplication Multiply the values of M and add the exponents, n. Multiply the units. 4.37 x 10 7 m x 6.17 x 10 13 s = (4.37 x 6.17) x 10 (7 + 13) (m x s) = 26.9629 x 10 20 ms = 2.69629 x 10 21 ms

13. Division Divide the values of M and subtract the exponents of the divisor from the exponent of the dividend. Divide the units. 7.9 x 10 9 m 4 3.1 x 10 6 m 3 7.9 7.9 = 3.1 x 10 (9 -6) m (4-3) = 2.548 x 10 3 m

14. Challenging Addition 8.9 x 10 5 m + 7.6 10 3 km = 8.9 x 10 5 m + 7600 x 10 3 m = 8.9 x 10 5 m + 76 x 10 5 m = (8.9 + 76) x 10 5 m = 84.9 x 10 5 m = 8.49 x 10 6 m or

15. Challenging Addition Cont. 8.9 x 10 5 m + 7.6 x 10 3 km = 0.0089 x 10 5 km + 7.6 x 10 3 km = 0.89 x 10 3 km + 7.6 x 10 3 km = 8.49 x 10 3 km 8.49 x 10 3 km = 8.49 x 10 6 m

16. Challenging Multiplication 2.7 x 10 10 μl X 4.3 x 10 -4 cl = 0.00027 x 10 10 cl X 4.3 x 10 -4 cl = (0.00027 x 4.3) x 10 (10-4) (cl x cl) = 0.001161 x 10 6 cl 2 = 1.161 x 10 3 cl 2

17. Challenging Division 6.2 x 10 8 kg 4.2 x 10 -5 Mg 6.2 x 10 8 kg 6.2 x 10 8 kg = 4200 x 10 -5 kg 6.2 6.2 = 4200 x 10 (8- -5) = 0.00147 x 10 13 = 1.47 x 10 10