Chapter 3 Scientific Measurement Understand scientific notation State the results of calculations to the appropriate number of significant figures Convert between metric units Match units or instruments with the proper measurement

Understand scientific notation To convert a number into scientific notation; move the decimal point so only 1 non-zero digit is to the left of the decimal point. if you move the decimal point to the left, the power of 10 will be positive. if you move the decimal point to the right, the power of 10 will be negative. 3,600 = 3.6 x 103 0.000 075 2 = 7.52 x 10-5 5,732,873.912 = ? 0.124 04 = ?

Understand scientific notation To convert a number out of scientific notation; if the power of 10 is positive move the decimal point to the right the power number of places if the power of 10 is negative move the decimal point to the left the power number of places. 8.1 x 10-5 = 0.000081 1.2 x 108 = 120000000 9.342 780 23 x 104 = ? 3.704 x 10-6 = ? Practice Problems Handout

State the results of calculations to the appropriate number of significant figures Accuracy: Measure of how close a measurement comes to the actual or true value Precision: Measure of how close a series of measurements are to one another Error: Experimental value – accepted value Percent error error x 100% accepted value

State the results of calculations to the appropriate number of significant figures (Stop: scientific notation and % error problems) A student measures the temperature of boiling water. The thermometer reads 99.1 oC. What is the error? Accepted value of boiling point of water is 100.0 oC 99.1 oC - 100.0 oC = -0.9 oC What is the percent error? -0.9 oC x 100% = 0.9% 100.0 oC

State the results of calculations to the appropriate number of significant figures Measured quantities in science have a degree of uncertainty due to the instrument being used. The measured number has to reflect that uncertainty. That is accomplished by using: Significant Figures (Sig Figs) In science, a measured quantity has two meanings: The numerical value (with the proper units) The sensitivity (uncertainty) of the measuring instrument: precision The number of sig figs is important in calculations Pg. 56: Figure 3.6

Rules for Counting Sig Figs State the results of calculations to the appropriate number of significant figures Rules for Counting Sig Figs Every nonzero digit represented in a measurement is significant. 24.7 m has 3 sig figs 0.4587 has 4 sig figs 134.798 has ? sig figs 0.6668 has ? sig figs Zeros appearing between non zero digits are significant. 7003 has 4 sig figs 0. 96501 has 5 sig figs 40.30609 has ? sig figs 0.306201 has ? sig figs

Rules for Counting Sig Figs State the results of calculations to the appropriate number of significant figures Rules for Counting Sig Figs Zeros ending a number to the right of the decimal point are significant 23.80 has 4 sig figs 0.130700 has 6 sig figs 1,006.00 has ? sig figs 0.34090 has ? sig figs Zeros starting a number or ending the number to the left of the decimal point are not counted as significant 16000 has 2 sig figs 0.0002709 has 4 sig figs 870,600 has ? sig figs 0.0450 has ? sig figs

Unlimited number of Sig Figs State the results of calculations to the appropriate number of significant figures Unlimited number of Sig Figs Specific whole numbers that are counted (vs measured) have unlimited numbers of significant figures. 23 people 4 fume hoods Exactly defined quantities have unlimited numbers of significant figures. 1 minute = 60 seconds 10 mm = 1 cm

General Rule for Counting Sig Figs State the results of calculations to the appropriate number of significant figures General Rule for Counting Sig Figs 1. Start on the left with the first nonzero digit. 2. End with the last nonzero digit OR with the last zero that ends the number to the right of the decimal point

Sig Figs in Calculations State the results of calculations to the appropriate number of significant figures Sig Figs in Calculations An answer cannot be more precise than the least precise measurement from which it was calculated! therefore Any mathematical calculation involving measured quantities must be rounded off to reflect the precision of the measurement!

Sig Fig Practice Problems How many sig figs in each measurement? 1. 123 meters 5. 30.0 meters 2. 0.123 meters 6. 22 meter sticks 3. 40,506 meters 7. 0.07080 meters 4. 9.8000 x 104 meters 8. 98000 1. 3 2. 3 3. 5 4. 5 5. 3 6. unlimited 7. 4 8. 2

Sig Fig Practice Problems How many sig figs: 1. 0.05730 meters 2. 8765 meters 3. 0.00073 meters 4. 1.072 meters 4 2. 4 3. 2 4. 4 Round each number to the number of sig figs shown: 314.721 meters (4) 2. 0.001755 meters (2) 1. 314.7 2. 0.0018

Practice Problems Round each to 2 sig figs and write in scientific notation. 87.073 meters 2. 4.3621 x 108 meters 3. 0.01552 meters 4. 9009 meters 8.71 x 101 2. 4.36 x 108 m 1.55 x 10-2 m 4. 9.01 x 103 m Go to Sig fig HO

State the results of calculations to the appropriate number of significant figures Sig Figs in Calculations: Addition & Subtraction The answer to an addition or subtraction calculation must be rounded to the same number of decimal places as the measurement with the least number of decimal places. 12.52 m + 349.0 m + 8.24 m = 369.76 m 12.52 has 2 decimal places; 349.0 has 1 decimal place; 8.24 has 2 decimal places The answer is rounded off to 1 decimal place = 369.8 m Practice problems Pg. 60: 9,10 on over head

State the results of calculations to the appropriate number of significant figures Sig Figs in Calculations: Multiplication & Division The answer to a multiplication or division calculation must be rounded to the same number of significant figures as the measurement with the least number of significant figures. 7.55 m x 0.34 m = 2.567 m2 7.55 has 3 sig figs; 0.34 has 2 sig figs The answer must be rounded to 2 sig figs = 2.6 m2 Practice: Pg. 61: Sample Problem 3-4, 11,12

Density Density is the ratio of an object’s mass to its volume. Density= Mass/Volume D = m/V units = g/cm3 (solid & liquid) or g/L (gases) Ex: a piece of lead has a volume of 10.0 cm3 and a mass of 114 g, what is it’s density? 114g/ 10.0cm3 = 11.4 g/cm3

Density Solving for other variables: V = m/D What is the volume of a 68g bar of silver with a density of 10.5 g/cm3? M= D x V There are two balloons, 10.0 L each, one contains helium (D=0.179 g/L), the other contains air (D=1.29g/L). How much less does the helium balloon weigh? GO TO DENSITY PRACTICE PROBLEM HO

STOP And Test 2014

Convert between metric units Quantity SI Unit Non-SI Unit Instrument Length meter (m) Ruler Mass gram (g) Balance Temperature Kelvin (K) oCelsius Thermometer Volume cubic meter liter Graduated Cylinder Buret Energy joule calorie Calorimeter Amount of mole substance

Convert between metric units Metric Prefixes kilo hecto deka one deci centi milli 1,000 100 10 1 0.1 0.01 0.001 (m,g,L) Mega Micro 1,000,000 0.000,000,1 Kids have dropped over dead converting metrics

Convert between metric units Metric Conversions Moving the decimal point If the unit is the same, use the saying to move the decimal (KHDODCM) Convert 4.15 kg to cg: Start at K and move to c. The decimal will be moved 5 places to the right to give 415,000 cg Convert 3,470 mL to L: Start at m and move to o. The decimal will be moved 3 places to the left to give 3.47 L Convert 3.00 cm to mm: Start at c and move to m. The decimal will be moved 1 place to the right to give 30.0 mm (include all sig figs!) Convert 756 g to mL: Can’t be done due to different units!

Metric Practice Problems Convert the following on your own paper: 1) 34.20 grams to milligrams 2) 0.00456 kilometers to meters 3) 6089 milliliters to kiloliters 4) convert 12.5 cm3 (centimeter cubed) to ml (milliliter) Answers: 1) 34200 mg 2) 4.56 m 3) 0.006089 kl 4) 12.5 ml = 12.5 cm3 because 1ml = 1cm3

Convert between metric units Volume Measurements & Conversions Metric volumes come in two forms: Liters or cubic meters Conversion between forms: 1 L = 1 dm3 and 1 mL = 1 cm3 Convert 3.45 L to cm3: 3.45 L = 3,450 mL = 3,450 cm3 Convert 0.784 dm3 to mL: 0.784 dm3 = 0.784 L = 784 mL Conversion within cubic form: 1 dm3 = 1,000 cm3 When converting within cubic volumes, multiply the number of places the decimal is moved by 3 Convert 2.56 m3 to cm3: Move the decimal two places to the right x 3 so a total of 6 places so 2,560,000 cm3 GO to Metric HO

Temperature Temperature is the measure of kinetic energy of particles in matter. Temperature determines the direction of heat transfer. Almost all substances expand with increasing temperature.

Temperature The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C. The Kelvin scale sets 0 K at absolute zero (the ° symbol is not used). One degree on the Kelvin scale is equal to one degree on the Celsius scale. 0 K = -273°C 0°C = 273 K K = °C + 273

Temperature Examples: Liquid nitrogen boils at 77.2 K. What is this temperature in °C? Silver melts at 960.8°C and boils at 2212°C. What is this temperature in degrees Kelvin?

Temperature Examples: Liquid nitrogen boils at 77.2 K. What is this temperature in °C? 77.2 – 273 = -196 Silver melts at 960.8°C and boils at 2212°C. What is this temperature in degrees Kelvin? Melting point: 960.8 + 273 = 1234 K, boiling point: 2212 + 273 = 2485 K