1. Practice: a) 27.68 cm –14.369 cm = b) 6.54 m x 0.37 m = c) 40.8 m 2  5.050 m =

2. Practice: a) 27.68 cm –14.369 cm = 13.311  13.31 b) 6.54 m x 0.37 m = 2.4198  2.4 c) 40.8 m 2  5.050 m = 8.07921  8.08 Raw Math ValueSig. Fig. Value

3. Scientific Notation Thursday, August 13 th, 2015 Textbook pages 63 – 65

4. Scientific Notation Scientific notation is way of writing numbers that are too big or too small to be conveniently written in decimal form

5. Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten ten 23 X 10 5 is not in proper scientific notation. Why? 23 X 10 5 is not in proper scientific notation. Why?

6. 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive. To write a number in scientific notation:

7. BIG Examples! 300 = 3 x 10 2 60,000 = 6 x 10 4 98,000,000 = 9.8 x 10 7 8657 = 8.657 x 10 3 250 = 36,700 = 785,000,000 = 99,000,000,000 =

9. Try These 4,000 2.48 X 10 3 6.123 X 10 6 306,000,000 5.70 x 10 5 Convert each from scientific notation into standard/long form or vice versa

10. small Examples! 0.02 = 2 x 10 -2 0.0065 = 6.5 x 10 -3 0.0000708 = 7.08 x 10 -5 0.000000001 = 1 x 10 -9 0.25 = 0.0036 = 0.00007001 = 0.00000003 =

11. Why does a Negative Exponent give us a small number? 10000 = 10 x 10 x 10 x 10 = 10 4 10000 = 10 x 10 x 10 x 10 = 10 4 1000 = 10 x 10 x 10 = 10 3 1000 = 10 x 10 x 10 = 10 3 100 = 10 x 10 = 10 2 100 = 10 x 10 = 10 2 10 = 10 1 1 = 10 0 1 = 10 0 Do you see a pattern?

12. Try These 0.00873 3.48 X 10 -4 0.1560.00000099 5.70 x 10 -6 Convert each from scientific notation into standard/long form or vice versa

13. 10,0039.57 x 10 -7 1.6 x 10 3 507,000,000 0.00013.301 x 10 5 6.1 x 10 10 1.8 x 10 -9 10,000,000,000 0.0045 Convert each from scientific notation into standard/long form or vice versa

14. Multiplication When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents. Sample Problem: Multiply (3.2 x 10 -3 ) (2.1 x 10 5 ) Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5 Answer: 6.7 x 10 2

15. Division Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6.4 x 10 6 ) by (1.7 x 10 2 ) Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2 Answer: 3.8 x 10 4

16. Addition and Subtraction To add or subtract numbers written in scientific notation, you must….express them with the same power of ten. Sample Problem: Add (5.8 x 10 3 ) and (2.16 x 10 4 ) Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5.8 x 10 3 =.58 x 10 4 so.58 x 10 4 + 2.16 x 10 4 =? Answer: 2.74 x 10 4