Scientific Notation & Scientific Notation & Round CalculationsRound Calculations

8/23/128/23/12

AgendaAgenda

BellworkBellwork Metric VideoMetric Video Measurement Activity Post LabMeasurement Activity Post Lab Scientific NotationScientific Notation Rounding CalculationsRounding Calculations

BellworkBellwork

Identify which of the following are Identify which of the following are prefix units:prefix units:

(a) N (b) cJ (c) (a) N (b) cJ (c) μμs (d) g (e) km (f) Ls (d) g (e) km (f) L Answer: (b) (c) and (e)Answer: (b) (c) and (e)

Domino Metric Conversions (step #4 - review)

For metric dominoes:

• The “multiplier” goes with the BASE unit,

• And “1” goes with the PREFIX unit

Metric Prefixes (review)

Prefix Prefix Symbol Multiplier

mega- M (unit) = 106 (base units)

kilo- k (unit) = 103 (base units)

BASE UNIT - 100 (1)

centi- c (unit) = 10-2 (base units)

milli- m (unit) = 10-3 (base units)

micro- μ (unit) = 10-6 (base units)

Measurement ActivityMeasurement Activity

Part 1: Was similar to historic Part 1: Was similar to historic measurement systemsmeasurement systems

Standard measurement systems date Standard measurement systems date back to the early 1800’sback to the early 1800’s

Measurement ActivityMeasurement Activity

Part 2: Estimation does have its use Part 2: Estimation does have its use when you can’t directly measure when you can’t directly measure somethingsomething

Measurement ActivityMeasurement Activity

Lab Bench HeightLab Bench Height 1 m1 m 10-11 dm10-11 dm 106 cm106 cm 106.3 cm 106.3 cm

or 1063 mmor 1063 mm

HallwayHallway 3 m3 m 3.0 m3.0 m 3.00 m3.00 m 2.997 m2.997 m

Historic English Units

• U.S. Length Units:– Point– Pica– Inch– Foot– Yard – Mile

Unit Divisions SI Equivalent

International

1 point (p) 352.777778 µm

1 pica (PI) 12 p 4.233333 mm

1 inch (in) 6 PI 25.4 mm

1 foot (ft) 12 in 0.3048 m

1 yard (yd) 3 ft 0.9144 m

1 mile (mi) 5280 ft or 1760 yd 1.609344 km

US Survey

1 link (li) 33⁄50 ft or 7.92 in 0.2012 m

1 (survey) foot (ft) 1200⁄3937 m 0.30480061 m

1 rod (rd) 25 li or 16.5 ft 5.02921 m

1 chain (ch) 4 rd 20.11684 m

1 furlong (fur) 10 ch 201.1684 m

1 survey (or statute) mile (mi) 8 fur 1.609347 km

1 league (lea) 3 mi 4.828042 km

Scientific NotationScientific Notation

Scientific NotationScientific Notation

Scientific NotationScientific Notation: A way to write very : A way to write very large or very small numbers in a large or very small numbers in a compact way compact way

Use scientific notation for numbers Use scientific notation for numbers larger then 10,000 and smaller then larger then 10,000 and smaller then 0.0010.001

Scientific NotationScientific Notation

The components of scientific notation:The components of scientific notation:8.238 x 108.238 x 10-31-31

““8.238” is the coefficient8.238” is the coefficient ““x 10” is the basex 10” is the base ““-31” is the exponent-31” is the exponent Where the coefficient has to be a Where the coefficient has to be a

number:number:1 1 ≤ coefficient < 10≤ coefficient < 10

Scientific NotationScientific Notation

The Andromeda Galaxy contains at The Andromeda Galaxy contains at about 200,000,000,000 stars. about 200,000,000,000 stars.

Mass of a dust particle is Mass of a dust particle is 0.000000000753 kg0.000000000753 kg . .

Scientific NotationScientific Notation

200,000,000,000 stars.200,000,000,000 stars. In scientific notation is:In scientific notation is:

2 x 102 x 101111 stars stars

Scientific NotationScientific Notation

0.000000000753 kg0.000000000753 kg In scientific notation is:In scientific notation is:

7.53 x 107.53 x 10-10-10

Decimal NotationDecimal Notation

Given: 3 x 10Given: 3 x 1066

Is: 3000000Is: 3000000 Given: 2.84 x 10Given: 2.84 x 10-7-7

Is: 0.000000284Is: 0.000000284

Rounding CalculationsRounding Calculations

Rounding to Sig. Figs.Rounding to Sig. Figs.

Multiplication and division of numbers Multiplication and division of numbers After the calculation, round the answer After the calculation, round the answer

to the number that has the to the number that has the leastleast amount of sig. figs.amount of sig. figs.

Note: Addition and subtraction have Note: Addition and subtraction have different rulesdifferent rules

Sig. Figs. Exceptions in Sig. Figs. Exceptions in CalculationsCalculations

Conversion factors (metric conversion)Conversion factors (metric conversion) Scaling factorsScaling factors Counting number (EX: number of trials Counting number (EX: number of trials

or number of students)or number of students) Round to sig. figs. At the END of a Round to sig. figs. At the END of a

calculationcalculation

Estimation vs. MeasurementEstimation vs. Measurement

Estimation:Estimation: Length: 17 mLength: 17 m Width: 7 mWidth: 7 m Height: 3 mHeight: 3 m Volume = 357 mVolume = 357 m33

Volume = 400 mVolume = 400 m33

Measurement:Measurement: Length: 14.53 mLength: 14.53 m Width: 9.56 mWidth: 9.56 m Height: 2.68 mHeight: 2.68 m Volume = 372.270224 mVolume = 372.270224 m33

Volume = 372 mVolume = 372 m33

What is the volume of the room?

Scientific Notation (calculators)Scientific Notation (calculators)

USE THE EXPONENT FUNCTIONUSE THE EXPONENT FUNCTION (4.8 x 10(4.8 x 10-6-6) / (5.134 x 10) / (5.134 x 10-19-19) =) = 9.349435138 x 109.349435138 x 101212

Displays will differDisplays will differ 9.3 x 109.3 x 101212 (2 sig. figs.) (2 sig. figs.)

Scientific NotationScientific Notation

When writing numbers in scientific notationWhen writing numbers in scientific notation

Express numbers as Express numbers as 4.71 x 104.71 x 10-61-61

4.714.71-61-61 ≠ 4.71 x 10 ≠ 4.71 x 10-61-61

4.714.71-61 -61 = 8.83 x 10= 8.83 x 10-42-42

4.71E-61 = 4.71 x 104.71E-61 = 4.71 x 10-61-61

Example #1Example #1

3.0 x 4.31 = 12.933.0 x 4.31 = 12.93 3.0 (2 sig. figs.)3.0 (2 sig. figs.) 4.31 (3 sig. figs.)4.31 (3 sig. figs.) Round to 2 sig. figs.Round to 2 sig. figs. Final answer is Final answer is 1313

Example #2Example #2

7000 / 13.37 = 523.5602094 7000 / 13.37 = 523.5602094 7000 (1 sig. figs.)7000 (1 sig. figs.) 13.87 (4 sig. figs.)13.87 (4 sig. figs.) Round to 1 sig. figs.Round to 1 sig. figs. Final answer is Final answer is 500500

Rest of ClassRest of Class

Work on HW: #71-82 due tomorrowWork on HW: #71-82 due tomorrow and #107-132 due Fridayand #107-132 due Friday