UNIT 1: TOOLS OF THE TRADE Math Skills Math Skills

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