Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Approximations of π wikipedia , lookup
Location arithmetic wikipedia , lookup
Principia Mathematica wikipedia , lookup
Large numbers wikipedia , lookup
Elementary mathematics wikipedia , lookup
Abuse of notation wikipedia , lookup
Bra–ket notation wikipedia , lookup
Mechanical calculator wikipedia , lookup
History of mathematical notation wikipedia , lookup
Musical notation wikipedia , lookup
Big O notation wikipedia , lookup
UNIT 1: TOOLS OF THE TRADE Math Skills Scientific Notation Abbreviation used by scientists to express extremely LARGE or SMALL numbers. Takes the form M x 10n where 1 ≤ M <10 – If “n” is positive, the number is LARGE. – If “n” is negative, the number is small. Examples of Scientific Notation Standard Form Scientific Notation 6,230,000,000 6.23 x 109 504,000 5.04 x 105 0.00000065 6.5 x 10-7 0.00028 2.8 x 10-4 Changing number into Scientific Notation Move the decimal point so there is only one nonzero digit to the left of it. 973,000,000 Count how many spots the decimal moved. This will be the “n” value. 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. 9.73 x 108 9.73 000 000 Changing Number from Scientific Notation to Standard Form Check if “n” is positive or negative. 3.62 x 10-4 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.) 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) 0.000362 Calculators and Scientific Notation Scientific calculators have a button to represent x10n Buttons can be: Exp EE E x10n Look at your calculator, what button does your calculator have? Entering Numbers on Calculator When entering a number in scientific notation, ALWAYS use (Exp, E, EE , x10n etc.) button. The multiplication sign does not need to be pressed. Example: 3.2 x 1023 Press 3 Press . Press 2 Press E, EE, Exp Press 23 Convert to Scientific Notation 1. 2. 3. 4. 5. 6. 0.00468 245,000,000 698,000 0.569 0.00000000758 893,000,000,000,000 1. 4.68 x 10-3 2. 2.45 x 108 3. 6.98 x 105 4. 5.69 x 10-1 5. 7.58 x 10-9 6. 8.93 x 1014 Convert to Standard Notation 1. 2. 3. 4. 5. 6. 10-5 8.32 x 4.258 x 108 2.0 x 10-2 6.6 x 104 5.23 x 10-9 1.9985 x 103 1. 0.0000832 2. 425,800,000 3. 0.02 4. 66,000 5. 0.00000000523 6. 1998.5 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 108) / (6.74 x 10-2) = a) 5.93 x 109 b. (6.70 x 1017) / (8.60 x 10-3) = b) 7.79 x 1019 c. (4.7 x 10-2) x (5.07 x 10-6) = c) 2.39 x 10-7 #5 More Practice a) (1.16 x 103) x (5.9 x 10-7) = 2.79 x 10-6 (2.45 x 102) b) (4.06 x 10-5) x (7.98 x 103) = 4.80x 102 (6.75 x 10-4) c) 10-11) (9.25 x (4 x 1026) x (7.5 x 10-15) -23 3.08 x 10 =