1. UNIT 1: TOOLS OF THE TRADE Math Skills Math Skills

2. Scientific Notation Abbreviation used by scientists to express extremely LARGE or SMALL numbers. Abbreviation used by scientists to express extremely LARGE or SMALL numbers. Takes the form M x 10 n Takes the form M x 10 n where 1 ≤ M <10 where 1 ≤ M <10 –If “n” is positive, the number is LARGE. –If “n” is negative, the number is small.

3. Examples of Scientific Notation Standard Form Scientific Notation 6,230,000,0006.23 x 10 9 504,0005.04 x 10 5 0.000000656.5 x 10 -7 0.000282.8 x 10 -4

4. Changing number into Scientific Notation Move the decimal point so there is only one nonzero digit to the left of it. Move the decimal point so there is only one nonzero digit to the left of it. 973,000,0009.73 000 000 973,000,0009.73 000 000 Count how many spots the decimal moved. This will be the “n” value. Count how many spots the decimal moved. This will be the “n” value. Decimal moved 8 spots to left Decimal moved 8 spots to left Remember if the number was large to begin with, “n” is going to be positive. If the number was small to begin with, “n” will be negative. Remember if the number was large to begin with, “n” is going to be positive. If the number was small to begin with, “n” will be negative. 9.73 x 10 8 9.73 x 10 8

5. Changing Number from Scientific Notation to Standard Form Check if “n” is positive or negative. Check if “n” is positive or negative. 3.62 x 10 -4 3.62 x 10 -4 If n is positive, move the decimal to the Right the same number of spaces of “n”’s value If n is positive, move the decimal to the Right the same number of spaces of “n”’s value (A positive “n” value indicates a LARGE number.) (A positive “n” value indicates a LARGE number.) If “n” is negative, move the decimal to the LEFT the same number of spaces of “n”’s value. If “n” is negative, move the decimal to the LEFT the same number of spaces of “n”’s value. (A negative “n” value indicates a SMALL number) (A negative “n” value indicates a SMALL number) 0.000362 0.000362

6. Calculators and Scientific Notation Scientific calculators have a button to represent x10 n Scientific calculators have a button to represent x10 n Buttons can be: Buttons can be: ExpEEEx10 n ExpEEEx10 n Look at your calculator, what button does your calculator have? Look at your calculator, what button does your calculator have?

7. Entering Numbers on Calculator When entering a number in scientific notation, ALWAYS use (Exp, E, EE, x10 n etc.) button. When entering a number in scientific notation, ALWAYS use (Exp, E, EE, x10 n etc.) button. The multiplication sign does not need to be pressed. The multiplication sign does not need to be pressed. Example: 3.2 x 10 23 Example: 3.2 x 10 23  Press 3  Press.  Press 2  Press E, EE, Exp  Press 23

8. Convert to Scientific Notation 1. 0.00468 2. 245,000,000 3. 698,000 4. 0.569 5. 0.00000000758 6. 893,000,000,000,000 1. 4.68 x 10 -3 2. 2.45 x 10 8 3. 6.98 x 10 5 4. 5.69 x 10 -1 5. 7.58 x 10 -9 6. 8.93 x 10 14

9. Convert to Standard Notation 1. 8.32 x 10 -5 2. 4.258 x 10 8 3. 2.0 x 10 -2 4. 6.6 x 10 4 5. 5.23 x 10 -9 6. 1.9985 x 10 3 1. 0.0000832 2. 425,800,000 3. 0.02 4. 66,000 5. 0.00000000523 6. 1998.5

10. 1. Calculate the answer using your calculator. Remember the x 10 part scientific notation is the same the EE or EXP button on your calculator. a. (4 x 10 8 ) / (6.74 x 10 -2 ) = b. (6.70 x 10 17 ) / (8.60 x 10 -3 ) = c. (4.7 x 10-2) x (5.07 x 10 -6 ) = a) 5.93 x 10 9 b) 7.79 x 10 19 c) 2.39 x 10 -7

11. #5 More Practice a) (1.16 x 10 3 ) x (5.9 x 10 -7 ) = (2.45 x 10 2 ) (2.45 x 10 2 ) b) (4.06 x 10 -5 ) x (7.98 x 10 3 ) = (6.75 x 10 -4 ) c) (9.25 x 10 -11 ) = (4 x 10 26 ) x (7.5 x 10 -15 ) 2.79 x 10 -6 4.80x 10 2 3.08 x 10 -23