Scientific Measurement

Measurements and Their Uncertainty Measurement – quantity that has both a number and unit Measurement – quantity that has both a number and unit - Example: your height, the temperature outside etc.

Measurements Measurements are fundamental to experimental sciences Measurements are fundamental to experimental sciences - important to decide if measurement is correct

Scientific Notation Scientific Notation – given number is written as product of two numbers Scientific Notation – given number is written as product of two numbers - a coefficient and ten raised to a power Example: 3,100,000 = 3.1 X = 1.1 X 10 -7

Accuracy vs. Precision Accuracy – measure of how close a measurement comes to actual or true value Accuracy – measure of how close a measurement comes to actual or true value - measured value must be compared to correct value Precision – measure of how close series of measurements are to each other Precision – measure of how close series of measurements are to each other - Consistent - must compare values of two or more repeated measurements

Accuracy vs. Precision

Determining Error Accepted value – the correct value based on reliable references Accepted value – the correct value based on reliable references Experimental Value – value measured in lab Experimental Value – value measured in lab Error – difference between experimental value and accepted value Error – difference between experimental value and accepted value

Determining Error Error = experimental value – accepted value Error = experimental value – accepted value Error can be positive or negative Error can be positive or negative Example: Example: - water in lab boils at 99.1˚C - water boils at accepted value of 100.0˚C Error = 99.1˚C – 100.0˚C = - 0.9°C Error = 99.1˚C – 100.0˚C = - 0.9°C

Percent Error Percent Error – absolute value of error divided by accepted value, multiplied by 100% Percent Error – absolute value of error divided by accepted value, multiplied by 100% Percent – comes from Latin words per, meaning “by” or “through” and centum, meaning “100” Percent – comes from Latin words per, meaning “by” or “through” and centum, meaning “100”

Percent Error Percent error = (|error| / accepted) X 100% Example: Example: Percent error = (|99.1˚C – 100.0˚C| / 100.0˚C) X 100% = (0.9˚C/100.0˚C) X 100% = X 100% = 0.9%

Significant Figures Significant Figures – all digits that are known, plus a last digit that is estimated Significant Figures – all digits that are known, plus a last digit that is estimated Measurements must be reported to correct number of significant figures Measurements must be reported to correct number of significant figures - calculated answers depend on number of significant figures

Rules For Significant Digits Every nonzero digit in reported measurement is assumed to be significant Every nonzero digit in reported measurement is assumed to be significant 24.7m and 0.743m = 3 sig. figs. Zeros between nonzero digits are significant Zeros between nonzero digits are significant 7003 m = 4 significant figures Leftmost zeros in front of nonzero digits are not significant only placeholders Leftmost zeros in front of nonzero digits are not significant only placeholders m = 2 significant figures = 9.9 X m

Rules for Significant Digits Zeros at end of a number and to the right of a decimal point are always significant Zeros at end of a number and to the right of a decimal point are always significant 1.010m and 9.000m = 4 sig. figs. Zeros at rightmost end of measurement lying to left of understood decimal point are not significant – only placeholders Zeros at rightmost end of measurement lying to left of understood decimal point are not significant – only placeholders 300m and 7000m = 1 sig. fig.

Rules for Significant Digits Two situations with unlimited number of significant figures: Two situations with unlimited number of significant figures: 1. Counting if you count 23 people, there are 23 people 2. Defined quantity 100cm = 1m

Significant Figures in Calculations A calculated answer cannot be more precise than least precise measurement from which it was calculated A calculated answer cannot be more precise than least precise measurement from which it was calculated

Rounding First decide on number of significant figures First decide on number of significant figures If number to the right of last know significant figure is less than five, drop the digit and keep it the same If number to the right of last know significant figure is less than five, drop the digit and keep it the same Example: 2.33 = 2.3 at 2 sig. figs. If number to the right of last know significant figure is 5 or greater increase by 1 If number to the right of last know significant figure is 5 or greater increase by 1 Example: 2.36 = 2.4 at 2 sig. figs.

Addition and Subtraction Answer to addition and subtraction calculation should be rounded to same number of decimal places as measurement with least number of decimal places Answer to addition and subtraction calculation should be rounded to same number of decimal places as measurement with least number of decimal places Example: Example: 12.52m m m = 369.8m = X 10 2 m

Multiplication and Division Round answer to same number of significant figures as measurement with least amount of significant figures Round answer to same number of significant figures as measurement with least amount of significant figures Example: Example: 7.55m X 0.34 m = 2.567m 2 = 2.6m 2

International System of Units SI – International System of Units SI – International System of Units - revised version of metric system - Five common base units include: - meter - kilogram - kelvin - second - mole

SI Base Units Quantity SI base unit Symbol Lengthmeterm Masskilogramkg TemperaturekelvinK Timeseconds Amount of Substance molemol Luminous intensity candelacd Electric Current ampereA

Common Metric Prefixes

Units of Length SI unit is meter (m) SI unit is meter (m) Common metric units include: Common metric units include: - centimeter - meter - kilometer

Metric Units of Length

Units of Volume SI unit is m 3 SI unit is m 3 Non-SI unit is liter (L) Non-SI unit is liter (L) Common metric units of volume include: Common metric units of volume include: - liter (L) - milliliter (mL) - cubic centimeter (cm 3 ) - microliter (µL)

Common Units of Volume

Units of Mass Basic SI unit is kilogram (kg) Basic SI unit is kilogram (kg) 1 gram (g) is 1/1000 of a kilogram 1 gram (g) is 1/1000 of a kilogram Common metric units of mass include: Common metric units of mass include: - kilogram (kg) - gram (g) - milligram (mg) - microgram (µg)

Units of Mass

Weight Weight – force that measures pull on given mass by gravity Weight – force that measures pull on given mass by gravity - different from mass

Units of Temperature Temperature – measure of how hot or cold and object is Temperature – measure of how hot or cold and object is - two common equivalent units: - Celsius - kelvin – SI unit

Kelvin scale vs. Celsius scale Celsius scale – places freezing point of water at 0˚C Celsius scale – places freezing point of water at 0˚C - boiling point of water at 100°C Kelvin scale – places freezing point of water at K Kelvin scale – places freezing point of water at K - boiling point of water at K Absolute zero = O kelvin (K) Absolute zero = O kelvin (K) - coldest possible temperature known

Kelvin vs. Celsius Example: Example: 10°C = 283 K 293 K = 20°C

Units of Energy Energy – capacity to do work or produce heat Energy – capacity to do work or produce heat - common units include joule and calorie - SI unit is joule (J)

Conversion Factors Conversion Factor – ratio of equivalent measurements Conversion Factor – ratio of equivalent measurements - multiplying by conversion factor changes numerical value - actual quantity size remains the same Example: 1000g/1kg and 1kg/1000g 10 9 nm/1m and 1m/10 9 nm

Dimensional Analysis Dimensional Analysis – way to analyze and solve problems using units or dimensions of measurements Dimensional Analysis – way to analyze and solve problems using units or dimensions of measurements - alternative approach to problem solving - page 82-83

Dimensional Analysis Example: Example: How many minutes are there in one week? 1 week X 7 days X 24 hours X 60 minutes 1 week 1 day 1 hour 1 week 1 day 1 hour = 10,080 minutes or X 10 4 minutes Complete practice problem number 29 Complete practice problem number 29 page 82 page 82

Dimensional Analysis Example: Example: - mass of copper available = 50.0g Cu - each student gets 1.84 g Cu - How many students are there? 50 g Cu X 1 student = = 27 students 1.84 g Cu Complete practice problems 30 and 31 (83) Complete practice problems 30 and 31 (83)

Converting Between Units Converting one unit to an equivalent measurement with another unit Converting one unit to an equivalent measurement with another unit Example: Example: mass = 750 dg 1g = 10dg Solve for the mass in grams. 750 dg X 1g = 75g 10dg 10dg Complete practice problem 32 and 33 page 84 Complete practice problem 32 and 33 page 84

Multistep Problems Example: length = cm = 7.3X10 -2 cm - convert to µm - convert to µm 10 2 cm = 1 m1m = 10 6 µm 7.3 X cm X 1m X 10 6 µm = 7.3 X 10 2 µm 10 2 cm 1m Complete 34 and 35 page 85 Complete 34 and 35 page 85

Converting Complex Units Example: density of manganese = 7.21g/cm g = 1kg 10 6 cm 3 = 1m 3 ? = kg/m g X 1kg X 10 6 cm 3 = 7.21 X 10 3 kg/m 3 1cm g 1m 3 Complete 36 and 37 page 86 Complete 36 and 37 page 86

Density Density – ratio of mass to volume of an object Density – ratio of mass to volume of an object Density = mass/volume Density = mass/volume

Density Density is an intensive property depending on composition of substance Density is an intensive property depending on composition of substance - does not depend on size of sample

Density Density of substance generally decrease as temp increases Density of substance generally decrease as temp increases Calculating Density: Calculating Density: mass = 3.1g volume = 0.35cm 3 Density = 3.1g/0.35cm 3 = g/cm 3 = 8.9 g/cm 3 (rounded to two significant figures) Complete number 46 and 47 (page 91) Complete number 46 and 47 (page 91)

Using Density to Calculate Volume Example: mass of coin = 14g density of silver = 10.5g/cm 3 volume of coin = ? Volume = mass/density 14g Ag X 1cm 3 Ag = 1.3cm 3 Ag 10.5g Ag 10.5g Ag Complete 48 and 49 – page 92 Complete 48 and 49 – page 92

Density Density = mass/volume Density = mass/volume Slope = (y/x) Slope = (y/x) Example: Example: 210 gram object 210 gram object 20mL volume of object 20mL volume of object Density = 210g/20mL = 10.5g/mL Density = 210g/20mL = 10.5g/mL