Scientific NotationScientific Notation

Write 17,500 in scientific notation.Write 17,500 in scientific notation.

1.75 x 101.75 x 1044

Write 0.0050 in scientific notation.Write 0.0050 in scientific notation.

5.0 x 105.0 x 10-3-3

(3.0 x 10(3.0 x 1055)(5.0 x 10)(5.0 x 10-2-2)= (3.0 x 5.0) x )= (3.0 x 5.0) x 10105+(-2)5+(-2)

3252

5

105.3105.3100.1

105.3xx

x

x

Addition and subtraction: all numbers Addition and subtraction: all numbers must be changed to the same exponent. must be changed to the same exponent. Then add or subtract the numbers, Then add or subtract the numbers, attaching the common exponent.attaching the common exponent.

ex.: 8.3 x 10ex.: 8.3 x 1022 + 5.7 x 10 + 5.7 x 1033

0.83 x 100.83 x 1033

++5.7 x 105.7 x 1033

6.53 x 106.53 x 1033 6.5 x 10 6.5 x 1033

Metric (SI) Base UnitsMetric (SI) Base Units

Length- meterLength- meter Mass- kilogramMass- kilogram Volume- liter (displacement)Volume- liter (displacement)

- cm- cm33 (L x W x H) (L x W x H) Temperature- Celsius C=5/9(F-32)Temperature- Celsius C=5/9(F-32)

F = 9/5C +32 F = 9/5C +32

- Kelvin 0- Kelvin 0◦◦C = 273 KC = 273 K

SI PrefixesSI Prefixes GigaGiga 101099

MegaMega 101066

kilokilo 101033

basic unitbasic unitdecideci 1010-1-1

centicenti 1010-2-2

millimilli 1010-3-3

micromicro 1010-6-6

nanonano 1010-9-9

picopico 1010-12-12

From DOE

Significant FiguresSignificant Figures

Indicate the uncertainty of a Indicate the uncertainty of a measurementmeasurement

The significant figures in a The significant figures in a measurement are all the digits that measurement are all the digits that are known with certainty, plus the are known with certainty, plus the first digit that is uncertain.first digit that is uncertain.

Significant FiguresSignificant Figures All nonzero digits are significant All nonzero digits are significant 43.543.5 Zeros are significant when. . .Zeros are significant when. . .

between two nonzero digits between two nonzero digits 120.01120.01 to the right of a decimal point and to the to the right of a decimal point and to the

right of a nonzero digit. right of a nonzero digit. 30.0030.00 to the left of an expressed decimal point to the left of an expressed decimal point

and to the right of a nonzero digit. and to the right of a nonzero digit. 19,000.19,000.

Not significant when. . . Not significant when. . . the zeros to the right of a decimal and to the zeros to the right of a decimal and to

the left of a nonzero digit. 0.000the left of a nonzero digit. 0.0005656 to the right of a nonzero digit but to the to the right of a nonzero digit but to the

left of an understood decimal left of an understood decimal 109109,000,000

Beginning zeros are not Beginning zeros are not significant.significant.

Ending zeros are only Ending zeros are only significant when there is a significant when there is a decimal.decimal.

Operations with significant Operations with significant figuresfigures

Multiplication and divisionMultiplication and divisionThe answer contains the same number of The answer contains the same number of

significant figures as the measurement significant figures as the measurement with the least number of with the least number of significant significant figuresfigures..

Addition and SubtractionAddition and Subtraction

The answer has the same number of The answer has the same number of decimal places as the measurement with the decimal places as the measurement with the least number of least number of decimal placesdecimal places..

Operations with significant Operations with significant figuresfigures

Multiplication and divisionMultiplication and division

Sample 1: 24 cm x 31.8 cm = 763.2 cmSample 1: 24 cm x 31.8 cm = 763.2 cm22

answer: 760 cmanswer: 760 cm22

Sample 2: 8.40 g ÷ 4.2 ml = 2 g/mlSample 2: 8.40 g ÷ 4.2 ml = 2 g/ml

answer: 2.0 g/mlanswer: 2.0 g/ml

Addition and SubtractionAddition and Subtraction

Sample 1: 49.1 g + 8.001 g = 57.101 Sample 1: 49.1 g + 8.001 g = 57.101 gg

answer: 57.1 ganswer: 57.1 g

Sample 2: 81.350 m – 7.35 m = 74 mSample 2: 81.350 m – 7.35 m = 74 m

answer: 74.00 manswer: 74.00 m

Precision vs. AccuracyPrecision vs. Accuracy

Precision is the agreement between Precision is the agreement between measurements.measurements.

Accuracy is the nearness of a Accuracy is the nearness of a measurement to its actual value.measurement to its actual value.

x xx

x xx

x xx

x

x x

Precise and accurate

Precise, not accurate

x x x

Not precise, nor accurate

These thermometers have different levels of precision. The increments on the left one are .2 but on the right one they are 1 . How should their temperatures be recorded?

5.8 37.53

Percent ErrorPercent Error

theoretical – experimentaltheoretical – experimental xx 100% =100% =

theoreticaltheoretical

Ex.: You analyze a sample of copper sulfate Ex.: You analyze a sample of copper sulfate and find that it is 68% copper. The and find that it is 68% copper. The theoretical value is 80%. What is your theoretical value is 80%. What is your percent error?percent error?

80-68 80-68 x 100% = 15%x 100% = 15%

8080

Derived UnitsDerived Units

Measurements derived from basic Measurements derived from basic units.units. Area= L x W (mArea= L x W (m22)) Volume = L x W x H (cmVolume = L x W x H (cm33)) Density = m/V (g/cmDensity = m/V (g/cm33))

CalculationsCalculations1. What is the density of a substance 1. What is the density of a substance

whose mass is 3.0 grams and its whose mass is 3.0 grams and its volume is 15cmvolume is 15cm33??

3.0 grams3.0 grams = = .20 g/cm.20 g/cm33

15 cm15 cm33 2. Cobalt has a density of 8.90 g/cm2. Cobalt has a density of 8.90 g/cm33. .

What volume would 17.8 g of cobalt What volume would 17.8 g of cobalt have?have?D=m/V soD=m/V so V=m/D V=m/D V = V = 17.8 g17.8 g = 2.00 cm = 2.00 cm33

8.90 g/cm8.90 g/cm33

Dimensional AnalysisDimensional Analysis

Multiply your starting point by a Multiply your starting point by a conversion factor (equal to 1)conversion factor (equal to 1)

Units should cross out algebraically, Units should cross out algebraically, leaving you with the unit desired.leaving you with the unit desired.

Ex.: Convert 2hr to min.Ex.: Convert 2hr to min.Conversion factor is 1hr = 60minConversion factor is 1hr = 60min

2hr x 2hr x 60min60min == 120 min 120 min 1 hr 1 hr

In Switzerland, gas prices are In Switzerland, gas prices are listed in Swiss Francs per liter. listed in Swiss Francs per liter. Convert the Swiss prices below Convert the Swiss prices below

to dollars per gallon.to dollars per gallon.

Conversion factors needed:Conversion factors needed: Dollars to Francs: 1 SF = $.83Dollars to Francs: 1 SF = $.83 Liters to gallons: 1 quart = 0.946 LLiters to gallons: 1 quart = 0.946 L

1 gallon = 4 quarts1 gallon = 4 quarts

1.71 SF1.71 SF x x $.83$.83 x x .946L.946L x x 4 qt4 qt = = $5.37$5.37

1 L 1 SF 1 qt 1 gal gal1 L 1 SF 1 qt 1 gal gal