Anything in black letters = write it in your notes (‘knowts’) Chapter 3 Scientific Measurement Anything in black letters = write it in your notes (‘knowts’)

Measurements without units are useless! 3.1 – Using & Expressing Measurements Measurements without units are useless! “I walked 5 today.” “The speed of light is 186,000 “I weigh 890” “20 of water” All measurements need units!

The coefficient must be between 1 and 10, exponent must be an integer. We will often work with really large or really small numbers in this class. Standard Notation Scientific Notation 872,000,000 grams 0.0000056 moles = 8.72 x 108 grams = 5.6 x 10-6 moles exponent coefficient 6.02 x 1023 The coefficient must be between 1 and 10, exponent must be an integer.

Multiplication and Division To multiply numbers written in scientific notation, multiply the coefficients and add the exponents. (3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106 (2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4

To divide numbers written in scientific notation, divide the coefficients and subtract the bottom exponent from the top exponent. Coefficient needs to be between 1 and 10

Addition and Subtraction When adding or subtracting in Sci. Not., the exponents must be the same. Not the same, need to adjust one of the exponents (5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103) = (5.4 + 0.80) x 103 = 6.2 x 103

Example Solve each problem and express the answer in scientific notation. a. (8.0 x 10–2) x (7.0 x 10–5) b. (7.1 x 10–2) + (5 x 10–3)

(8.0 x 10–2) x (7.0 x 10–5) = (8.0 x 7.0) x 10–2 + (–5) = 56 x 10–7 a. Multiply the coefficients and add the exponents. (8.0 x 10–2) x (7.0 x 10–5) = (8.0 x 7.0) x 10–2 + (–5) = 56 x 10–7 = 5.6 x 10–6

b. Rewrite one of the numbers so that the exponents match. Then add the coefficients (7.1 x 10–2) + (5 x 10–3) = (7.1 x 10–2) + (0.5 x 10–2) = (7.1 + 0.5) x 10–2 = 7.6 x 10–2

Accuracy - closeness of a measurement to the actual or accepted value. Precision - closeness of repeated measurements to each other

Accuracy and Precision Darts on a dartboard illustrate the difference between accuracy and precision. Poor Accuracy, Poor Precision Good Accuracy, Good Precision Poor Accuracy, Good Precision The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.

Error Suppose you measured the melting point of a compound to be 78°C The actual melting point value (from reference books) is 76°C. The error in your measurement would be 2°C. Error = experimental value – accepted value Error is how far off your measurement is from the actual or known value.

How far off you are in a measurement doesn’t tell you much. For example, lets say you have $1,000,000 in your checking account. When you balance your checkbook at the end of the month, you find that you are off by $175; error = $175 Now, lets be more realistic, you have $225 in your checking account and after balancing you are off by $175!

Percent error compares the error to the size of the measurements. In both cases, there is an error of $175. But in the first, the error is such a small portion of the total that it doesn’t matter as much as the second. So, instead of error, percent error is more valuable. Percent error = error accepted value 100% x Percent error compares the error to the size of the measurements.

ASSIGN: Chapter 3 Worksheet #1

30.2°C In any measurement, the last digit is estimated Significant Figures In any measurement, the last digit is estimated 30.2°C The 2 is estimated (uncertain) by the experimenter, another person may say 30.1 or 30.3

9.3 mL 0.72 cm

Increasing Precision

The significant figures in a measurement include all of the digits that are known, plus the last digit that is estimated. Numbers that are NOT significant are called placeholders.

HOLY SMOKES!! Rules for determining Significant Figures (p. 67) 1. Every nonzero digit in a reported measurement is assumed to be significant. 2. Zeros appearing between nonzero digits are significant. 3. Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros. 4. Zeros at the end of a number and to the right of a decimal point are always significant. 5. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number. 5 (continued). If such zeros were known measured values, then they would be significant. Writing the value in scientific notation makes it clear that these zeros are significant. 6. There are two situations in which numbers have an unlimited number of significant figures. The first involves counting. A number that is counted is exact. 6 (continued). The second situation involves exactly defined quantities such as those found within a system of measurement. HOLY SMOKES!!

A shorter method for determining which numbers are significant in a measurement. All nonzero numbers are significant. Zeros are also significant if they are NOT placeholder zeros. Counted and exact numbers have an unlimited number of sig figs. The Tischer Method!™ A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is.

Underline the zeros that are placeholders 100 1.00 0.23 0.0034 1.01 1005.4 0.10 100.0 54.0 A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is. Zeros to the right of a number & after the decimal are more than placeholders, they are part of the measurement and are significant.

How many significant digits are in the following measurements? a) 150.31 grams b) 10.03 mL c) 0.045 cm d) 4.00 lbs e) 0.01040 m f) 100.10 cm g) 100 grams h) 1.00 x 102 grams i) 11 cars j) 2 molecules All nonzero numbers are significant. Zeros are also significant if they are NOT placeholders. Counted and exact numbers have an unlimited number of sig. figs.

Another Shorter Method “Box and Dot” Method for Counting Sig Figs 1. Draw a box around all digits from the 1st nonzero digit on left to last nonzero digit on the right. 2. If a dot is present, draw a box around any trailing zeros. 3. Any boxed digit is significant. Another Shorter Method SOURCE: JCE Vol 86 No 8 (Aug ‘09) W. Kirk Stephenson

A answer can’t be more accurate than the measurements it was calculated from

Rules for Add/Subtracting Sig Figs The answer to an +/- calculation should be rounded to the same number of decimal places as the measurement with the least number of decimal places. 3.2 cm 37.10 g

Rules for Mult/Division Sig Figs The answer to a x/÷ calculation should be rounded to the same number of sig figs as the measurement with the least number of sig figs. 3.8 cm2

ASSIGN: Chapter 3 Worksheet #2 Always round your final answer off to the correct number of significant digits. ASSIGN: Chapter 3 Worksheet #2

3.2 – Units of Measurement SI – International System of Units SI Base Units (page 74) Quantity SI base unit Symbol Length meter m Mass kilogram kg Temperature kelvin K Time second s Amount of substance mole mol Luminous intensity candela cd Electric current ampere A We will use all of these in this class How is Mass different from Amount of Substance?

Commonly Used Metric Prefixes (page 75) Symbol Meaning Factor mega M 1 million times larger than the unit it precedes 106 kilo k 1000 times larger than the unit it precedes 103 deci d 10 times smaller than the unit it precedes 10-1 centi c 100 times smaller than the unit it precedes 10-2 milli m 1000 times smaller than the unit it precedes 10-3 micro μ 1 million times smaller than the unit it precedes 10-6 nano n 1 billion times smaller than the unit it precedes 10-9 pico p 1 trillion times smaller than the unit it precedes 10-12

Volume - Amount of space occupied by an object (remember?) Normal units used for volume: Solids – m3 or cm3 Liquids & Gases – liters (L) or milliliters (mL) 1 L = 1000 mL 1 mL = 1 cm3 The volume of a material changes with temperature, especially for gases.

Mass - Weight - Measure of inertia (remember?) Force of gravity on a mass; measured in pounds (lbs) or Newtons. Weight can change with location, mass does not

1 cal = 4.184 J Energy – Ability to do work or produce heat. Normal units used for energy: SI – joule (J) non-SI – calorie (cal) 1 cal = 4.184 J How many joules are in a kilojoule? How many calories are in a kilocalorie?

Temperature – measure of how cold or hot an object is.

K = °C + 273 yucky! Temperature – measure of the average kinetic energy of molecules. Normal units used for temp: SI – kelvin (K) non-SI – celsius (°C) or Fahrenheit (°F) yucky! K = °C + 273

Celsius Kelvin 100 divisions 100°C Boiling point of water 373.15 K 0°C Freezing point 273.15 K

Density is an intensive property mass volume Density = Density is an intensive property Normal units for density: g/cm3, g/mL, g/L

Densities of Some Common Materials Solids and Liquids Gases Material Density at 20°C (g/cm3) Density at 20°C (g/L) Gold 19.3 Chlorine 2.95 Mercury 13.6 Carbon dioxide 1.83 Lead 11.3 Argon 1.66 Aluminum 2.70 Oxygen 1.33 Table sugar 1.59 Air 1.20 Corn syrup 1.35–1.38 Nitrogen 1.17 Water (4°C) 1.000 Neon 0.84 Corn oil 0.922 Ammonia 0.718 Ice (0°C) 0.917 Methane 0.665 Ethanol 0.789 Helium 0.166 Gasoline 0.66–0.69 Hydrogen 0.084

ASSIGN: Read 3.2 Lesson Check 3.2; #23-35 (page 82)

4.184 Joules = _______ calorie 3.3 – Solving Conversion Problems 12 inches = ______ foot 1 minute = _____ seconds 10 cents = _______ dime 24 hours = ______ day 1 km = ________meters 4.184 Joules = _______ calorie Fill in the blanks… These can all be used as conversion factors

Conversion Factors When two measurements are equal, they can be used as conversions between units. 1000 g 1 kg and Conversion factors 1 mile 5280 feet and 60 min 1 hour

Method used to convert measurements to other units. Dimensional Analysis Method used to convert measurements to other units. Start with given information. Use conversion factors to cancel units until desired unit is left.

How many seconds are in 8 hours? Example 1 How many seconds are in 8 hours? Start with given information. Use conversion factors to cancel units until desired unit is left. 60 min = 1 hr; 60 sec = 1 min Multiply across the top, divide along the bottom of the conversion factors.

How many km are in 25 miles? Example 2 Start with given information. Use conversion factors to cancel units until desired unit is left. 1.6 km = 1 mile Multiply across the top, divide along the bottom of the conversion factors.

5.26 mumu = 8 nunu; 1.76 nunu = 12.35 fufu; 0.826 fufu = 1035 bubu. Example 3 – TRY IT! 5.26 mumu = 8 nunu; 1.76 nunu = 12.35 fufu; 0.826 fufu = 1035 bubu. 1. How many mumus are in 10 bubus?

5.26 mumu = 8 nunu; 1.76 nunu = 12.35 fufu; 0.826 fufu = 1035 bubu. Example 4 – TRY IT! 5.26 mumu = 8 nunu; 1.76 nunu = 12.35 fufu; 0.826 fufu = 1035 bubu. 2. How many fufus are in 26 mumus?

A student converted 10.1 feet as follows: How many significant digits should the answer have? Why not 1?

ASSIGN: Chapter 3 Worksheet 3

Conversion Factor Quiz Show your WORK for credit. 1 horsepower = 745.7 W 2.54 cm = 1 inch LEFT: 1. Convert 6.5 horsepower into watts RIGHT: 1. Convert 100 watts into horsepower LEFT: 2. How many cm are in 12 miles? RIGHT: 2. How many cm are in 20 miles