Scientific Notation Write 17,500 in scientific notation. 1.75 x 104 (3.0 x 105)(5.0 x 10-2)= (3.0 x 5.0) x 105+(-2)

Addition and subtraction: all numbers must be changed to the same exponent. Then add or subtract the numbers, attaching the common exponent. ex.: 8.3 x 102 + 5.7 x 103 0.83 x 103 +5.7 x 103 6.53 x 103 6.5 x 103

Metric (SI) Base Units Length- meter Mass- kilogram Volume- liter (displacement) - cm3 (L x W x H) Temperature- Celsius C=5/9(F-32) F = 9/5C +32 - Kelvin 0◦C = 273 K Time- sec Amount of substance- mole

SI Prefixes Giga 109 Mega 106 kilo 103 basic unit deci 10-1 centi 10-2 milli 10-3 micro 10-6 nano 10-9 pico 10-12 Bobby measures a stick and says it is 5. Billy measures the same stick and says it is 15. They are both right. How can that be? UNITS!!!

From DOE

Indicate the uncertainty of a measurement Significant Figures Indicate the uncertainty of a measurement If the earth is 4 billion years old, will it be 4 billion and one next year? If I ask you how tall you are and you say between 5-6 feet, that isn’t very interesting. You left out the interesting information.

The significant figures in a measurement are all the digits that are known with certainty, plus the first digit that is uncertain. Read the bottom of the meniscus (line AB). 26.70ml

Significant Figures All nonzero digits are significant 43.5 Zeros are significant when. . . between two nonzero digits 120.01 to the right of a decimal point and to the right of a nonzero digit. 30.00 to the left of an expressed decimal point and to the right of a nonzero digit. 19,000. Not significant when. . . the zeros to the right of a decimal and to the left of a nonzero digit. 0.00056 to the right of a nonzero digit but to the left of an understood decimal 109,000

Beginning zeros are not significant. Ending zeros are only significant when there is a decimal.

Operations with significant figures Multiplication and division The answer contains the same number of significant figures as the measurement with the least number of significant figures. Addition and Subtraction The answer has the same number of decimal places as the measurement with the least number of decimal places.

Operations with significant figures Multiplication and division Sample 1: 24 cm x 31.8 cm = 763.2 cm2 answer: 760 cm2 Sample 2: 8.40 g ÷ 4.2 ml = 2 g/ml answer: 2.0 g/ml

Addition and Subtraction Sample 1: 49.1 g + 8.001 g = 57.101 g answer: 57.1 g Sample 2: 81.350 m – 7.35 m = 74 m answer: 74.00 m

Precision vs. Accuracy Precision is the agreement between measurements. Accuracy is the nearness of a measurement to its actual value. x x x x x x x x x x x x x x Not precise, nor accurate Precise, not accurate Precise and accurate

37.53  5.8  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?

Percent Error theoretical – experimental x 100% = theoretical Ex.: You analyze a sample of copper sulfate and find that it is 68% copper. The theoretical value is 80%. What is your percent error? 80-68 x 100% = 15% 80

Derived Units Measurements derived from basic units. Area= L x W (m2) Volume = L x W x H (cm3) Density = m/V (g/cm3)

Calculations 1. What is the density of a substance whose mass is 3.0 grams and its volume is 15cm3? 3.0 grams = .20 g/cm3 15 cm3 2. Cobalt has a density of 8.90 g/cm3. What volume would 17.8 g of cobalt have? D=m/V so V=m/D V = 17.8 g = 2.00 cm3 8.90 g/cm3

Dimensional Analysis Multiply your starting point by a conversion factor (equal to 1) Units should cross out algebraically, leaving you with the unit desired. Ex.: Convert 2hr to min. Conversion factor is 1hr = 60min 2hr x 60min = 120 min 1 hr

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

Conversion factors needed: Dollars to Francs: 1 SF = $.83 Liters to gallons: 1 quart = 0.946 L 1 gallon = 4 quarts 1.71 SF x $.83 x .946L x 4 qt = $5.37 1 L 1 SF 1 qt 1 gal gal