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UNIT 1: TOOLS OF THE UNIT 1: TOOLS OF THE TRADETRADE
Math SkillsMath Skills
Scientific NotationScientific Notation
Abbreviation used by scientists to Abbreviation used by scientists to express extremely express extremely LARGELARGE or or SMALL SMALL numbers.numbers.
Takes the form M x 10Takes the form M x 10nn
where 1 ≤ M <10where 1 ≤ M <10
– If “n” is positive, the number is LARGE.If “n” is positive, the number is LARGE.– If “n” is negative, the number is small.If “n” is negative, the number is small.
Examples of Scientific Examples of Scientific NotationNotation
Standard FormStandard Form Scientific Scientific NotationNotation
6,230,000,0006,230,000,000 6.23 x 106.23 x 1099
504,000504,000 5.04 x 105.04 x 1055
0.000000650.00000065 6.5 x 106.5 x 10-7-7
0.000280.00028 2.8 x 102.8 x 10-4-4
Changing number into Scientific Changing number into Scientific NotationNotation
Move the decimal point so there is only Move the decimal point so there is only oneone nonzero digit to the left of it. nonzero digit to the left of it.
973,000,000973,000,000 9.73 000 0009.73 000 000 Count how many spots the decimal Count how many spots the decimal
moved. This will be the “n” value.moved. This will be the “n” value. Decimal moved 8 spots to leftDecimal moved 8 spots to left Remember if the number was large to Remember if the number was large to
begin with, “n” is going to be begin with, “n” is going to be positivepositive. If . If the number was small to begin with, “n” the number was small to begin with, “n” will be will be negativenegative..
9.73 x 109.73 x 1088
Changing Number from Scientific Notation to Changing Number from Scientific Notation to Standard FormStandard Form Check if “n” is positive or negative.Check if “n” is positive or negative. 3.62 x 103.62 x 10-4-4
If n is positive, move the decimal to the If n is positive, move the decimal to the RightRight the the same number of spaces of “n”’s valuesame number of spaces of “n”’s value
(A positive “n” value indicates a (A positive “n” value indicates a LARGELARGE number.) number.) If “n” is negative, move the decimal to the If “n” is negative, move the decimal to the LEFT LEFT
the same number of spaces of “n”’s value.the same number of spaces of “n”’s value. (A negative “n” value indicates a (A negative “n” value indicates a SMALL SMALL number)number) 0.0003620.000362
Calculators and Scientific NotationCalculators and Scientific Notation
Scientific calculators have a button Scientific calculators have a button to represent to represent x10x10nn
Buttons can be:Buttons can be: ExpExp EEEE EE x10x10nn
Look at your calculator, what button Look at your calculator, what button does your calculator have?does your calculator have?
Entering Numbers on CalculatorEntering Numbers on Calculator When entering a number in scientific notation, When entering a number in scientific notation,
ALWAYSALWAYS useuse (Exp, E, EE , (Exp, E, EE , x10x10n n etc.) button.etc.) button.
The multiplication sign does not need to be The multiplication sign does not need to be pressed.pressed.
Example: 3.2 x 10Example: 3.2 x 102323
Press 3Press 3 Press .Press . Press 2Press 2 Press E, EE, ExpPress E, EE, Exp Press 23Press 23
Convert to Scientific Convert to Scientific NotationNotation
1.1. 0.004680.00468
2.2. 245,000,000245,000,000
3.3. 698,000698,000
4.4. 0.5690.569
5.5. 0.000000007580.00000000758
6.6. 893,000,000,000,00893,000,000,000,0000
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 Convert to Standard NotationNotation
1.1. 8.32 x 108.32 x 10-5-5
2.2. 4.258 x 104.258 x 1088
3.3. 2.0 x 102.0 x 10-2-2
4.4. 6.6 x 106.6 x 1044
5.5. 5.23 x 105.23 x 10-9-9
6.6. 1.9985 x 101.9985 x 1033
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 1. Calculate the answer using your calculator. Remember the calculator. Remember the x 10 x 10 part part
scientific notation is the same the EE or scientific notation is the same the EE or EXP button on your calculator.EXP button on your calculator.
a.a. (4 x 10(4 x 1088) ) // (6.74 x 10 (6.74 x 10-2-2) = ) =
b. (6.70 x 10b. (6.70 x 101717) ) // (8.60 x 10 (8.60 x 10-3-3) ) = =
c. (4.7 x 10-2) x (5.07 x 10c. (4.7 x 10-2) x (5.07 x 10-6-6) ) = =
a) 5.93 x 109
b) 7.79 x 1019
c) 2.39 x 10-7
#5 More Practice#5 More Practice
a)a) (1.16 x 10 (1.16 x 1033) x (5.9 x 10) x (5.9 x 10-7-7)) = = (2.45 x 10(2.45 x 1022) )
b)b) (4.06 x 10 (4.06 x 10-5-5) x (7.98 x 10) x (7.98 x 1033) ) = = (6.75 x 10(6.75 x 10-4-4))
c) c) (9.25 x 10 (9.25 x 10-11-11) ) = = (4 x 10(4 x 102626) x (7.5 x 10) x (7.5 x 10-15-15))
2.79 x 10-6
4.80x 102
3.08 x 10-23