5.1 - Scientific Notation & Units Measurements & Calculations 5.1 - Scientific Notation & Units

Scientific Notation Allows us to write very big and very small numbers

Scientific Notation Every number written in scientific notation has two basic parts.  The coefficient (first part) is always a decimal number between 1.00 and 9.99… The second part is 10 times some exponent

Scientific Notation 3.42 x 106 or 8.005 x 10-3 Notice that in each of these, the coefficient is a decimal number between 1.00 and 9.99…

Scientific Notation 3.42 x 106 means 3.42 x (10 x 10 x 10 x 10 x 10 x 10)   or 3,420,000

Scientific Notation 8.005 x 10-3 means 8.005 x (0.1 x 0.1 x 0.1)  or 0.008005

Scientific Notation the exponent on the 10 tells you which direction to move the decimal and how many times it should be moved. POSITIVE EXPONENT means > 1 (right) NEGATIVE EXPONENT means < 1 (left)

Scientific Notation Can I change standard notation to scientific notation? Let's say you wanted to convert the following number to scientific notation: 0.00000782

Scientific Notation The first part has to be between 1.00 and 9.99... Move your decimal until you have a number that qualifies 7.82

Scientific Notation Remember that the exponent tells you the number of spaces that you moved it.  So the answer is either 7.82 X 106 or 7.82 X 10-6

Scientific Notation A standard notation number LOWER than 1 means NEGATIVE exponent A standard notation number GREATER than 1 means POSITIVE exponent

Scientific Notation 1) 3,400 2) 0.000023 3) 101,000 4) 0.010

Exponential Notation A numerical system in which numbers are expressed in the form A × 10n where A is a number with a single nonzero digit to the left of the decimal place and n is a whole number. A is the coefficient n is a whole number 13

Converting from Decimal to Scientific Notation The decimal point in the decimal number is moved to the position behind (to the right of) the first nonzero digit. The exponent for the exponential term is equal to the number of places the decimal point has moved. 300. written as 3.00 × 102 (three sig figs) 0.004890 written as 4.890 × 10–3 (four sig figs) 14

Multiplication Using Scientific Notation (2.5 x 104)(2.0 x 102) = Multiply the coefficients 2.5 x 2.0 = 5.0 Add the exponents 104 + 102 = 106 Ans: 5.0 x 106

Division Using Scientific Notation (6.0 x 105) (2.0 x 102) = Divide the coefficients 6.0 2.0 = 3.0 Subtract the exponents 105 ̶ 102 = 103 Ans: 3.0 x 103 : :

Addition Using Scientific Notation (2.0 x 103) + (2.0 x 102) = Convert so that all exponents are the same 2.0 x 102 = 0.20 x 103 Add coefficients 2.0 x 103 + 0.20 x 103 Ans: 2.2 x 103

Addition Using Scientific Notation (4.0 x 107) ̶ (8.0 x 105) = Convert so that all exponents are the same 8.0 x 105 = 0.080 x 107 Subtract coefficients 4.0 x 107 ̶ 0.080 x 107 Ans: 3.92 x 107

Scientific Notation 5) 45.01 6) 1,000,000 7) 0.00671 8) 4.50

Homework Complete Scientific Notation Worksheet Watch video on unit conversion