Scientific Measurement

Measurements

• Quantities with both a number and a unit– Used to measure a physical property– .5 grams• Mass

– 2 liters• Volume

– 1.6 meters • Length

Why does this matter?

• In chemistry, we make lots of measurements– Examples?

• We need to have a common language of measurement so that we can understand each other’s results.

Scientific Notation

• In chemistry, we deal with numbers that are very big and very small– How many water molecules are in the beaker?• 600,000,000,000,000,000,000,000

– What is the width of a water molecule?• .0000000005 meters

Scientific Notation• How can we express big and small numbers in

a simpler way? – Powers of 10• 10 = 101 1 = 100 • 100 = 102 0.1 = 10-1

• 1000 = 103 0.01 = 10-2

• 10,000 = 104 0.001 = 10-3

– Exponent = # of places you move the decimal point to get behind the first digit• Left = positive• Right = negative

Scientific notation

Practice problem

• Express the following numbers in exponential form:– 100,000– 100– 0.001– .1– 1

Scientific notation

• To put a number in scientific notation, express it as the product of– A number between 1 and 10– A power of 10Example: • 5000 meters = 5 x 1000 meters

= 5 x 103 meters

• .025 liters = 2.5 x .01 liters = 2.5 x 10-2 liters

Practice problems

• Express the following numbers in scientific notation: – 5280 feet– 0.00042 grams– 602,000,000,000,000,000,000,000 atoms

Accuracy v. Precision

• Accuracy = how close your measurements are to the correct value– Ex: I can run a mile in 7 minutes• If you measure my mile time and get 7 minutes, you are

highly accurate• If you measure my time and get 8 minutes you are

inaccurate

Precision

• Precision = how close your measurements are to each other– If you measure my mile time and get 7 minutes

three times, you are very precise– If you measure my mile time and get 8 minutes

three times, you are still very precise• But you are not very accurate.

Accuracy v. Precision

Error

• Error is the difference between your measurement and the accepted value

Error = experimental value – accepted value

Practice problem

• Calculate the error:– Experimental value = 1 meter• Accepted value = 1.02 meters

– Experimental value = 10.7 seconds• Accepted value = 10.5 seconds

Percent Error

• How much error is a lot of error?– If my measurement of the weight of a car is 10 lbs

too much, do I care?– If my measurement of the weight of a baby is 10

lbs too much, do I care?

Percent error

• Percent error is an expression of error as a percentage of the accepted value

x 100%

Percent error practice

• Mr. Tunney’s new car weighs 2795 lbs. The dealership weighs the car at 2805 lbs. – What is the error? What is the percent error?

• When Mr. Tunney was born, he weighed 9.5 lbs. The doctor weighed him at 19.5 lbs.– What is the error? What is the percent error?

Percent error practice

• Felipe sticks a thermometer in a pot of boiling water, and measures its temperature as 99.1°C. The true temperature of boiling water is 100°C. – What is Felipe’s error? What is his percent error?

Significant Figures

• The accuracy of our measurements is limited by the accuracy of our tools

• What’s the smallest increment marked on this scale?

Significant Figures

• When making measurements, you can record as many digits as your tool measures, and you can estimate one more digit.

• All of these digits have useful information, so they are called significant figures

Significant figures?

• Can I measure this length as 11.754325 cm?

• Why/why not?• How many significant figures should this

measurement have?

Significant figure rules

• How do I know how many significant figures a given measurement has?– Example: I tell you I am 1.650 meters tall. How many

significant figures are there?• Rules: – All nonzero digits are significant– All zeroes between nonzero digits are significant– Leftmost zeroes are not significant– Rightmost zeroes are significant if they follow a

decimal point or are followed by a decimal point

Significant Figures Rules

• All nonzero digits are significant– How many significant figures:– 220– 1000– 345

Significant figure rules

• All zeroes between nonzero digits are significant– How many sig. figs?– 202– 1050– 10,002

Significant Figures Rules

• Leftmost zeroes are not significant– How many sig. figs?– 100– 0245– 0.003– 1.01

Homework 9/30

• 13) Error = -1.6°C, Percent error = 1.3%

• 14) a. unlimited b. 5 c. 3 d. 3

• 15) 6.6 x 104 b. 4.0 x 10-7 c. 107 d. 8.65 x 10-1 e. 1.9 x 1014

Significant Figures Rules

• Zeroes at the end of a number to the right of a decimal point are significant– How many sig. figs?– 1.00– 0.01– 0.203400

• Zeroes at the end of a number are also significant if they are followed by a decimal point– How many sig figs?– 10200– 10200.– 1030.00

Significant Figures Rules

• Countable or standard measurements have infinite sig. figs– How many sig. figs? – 4 apples– 60 seconds/minute

Significant Figures in Calculations

• In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.

Addition and Subtraction

• Round your answer to the largest digit that is the least significant digit of one of your measurements– Example: 12.52

349.0 + 8.24 369.76

Answer = 369.7

Multiplication and Division

• Round your answer to the same number of sig. figs as the term with the least number of sig. figs

175 m x 0.1 m = 17.5 m

Answer = 20 m

Practice problems

The Metric System

• The metric system is an international system of units designed to make measurements simple and easy– The five metric units we’ll use in class are• Meters• Grams• Kelvins• Seconds• Moles

Meters and Seconds

• Meters (m) are the metric unit of distance– 1 meter ≈ 3.3 feet

• Seconds (s) are the metric unit of time

Grams

• Grams (g) are the metric unit of mass– A paperclip weighs about 1 gram

Kelvins

• A kelvin (K) is the metric degree of temperature– 1 degree Kelvin = 1 degree Celsius– BUT the Kelvin scale starts at the lowest

temperature possible, -273°C– To convert from Celsius to Kelvin, subtract 273.

Moles

• A mole is the metric unit of quantity– 1 mole = 6.02 x 1023

– Very large, usually used for talking about how many atoms or molecules are in an object.

Metric prefixes• We can use a standard set of prefixes to make the

scale of metric units more convenient – Mega = 1 million times the unit– Kilo = 1 thousand times the unit– Hecto = 100 times the unit– Deka = 10 times the unit– Deci = 1/10 of the unit– Centi = 1/100 of the unit– Milli = 1/1000 of the unit– Micro = 10-6 of the unit– Nano = 10-9 of the unit– Pico = 10-12 of the unit

Volume

• Volume is the amount of space an object occupies. Volume = length x width x height

• The most common units we’ll use are a cubic centimeter (cm3) and a liter (L)– A liter equals 1000 cm3

Energy

• Energy is the capacity to do work or produce heat– The Joule (J) is the metric unit of energy. – The calorie is another (non-metric) unit of energy– 1 calorie = 4.18 Joules

Homework 10/3

• 21) a. 1/1000 or 10-3 b. 10-9 c. 1/10 or 10-1 d. 1/100 or 10-2

• 22) m3, L, dL, cL, mL, μL• 23) 8.8 x 102 cm3

• 25) C = K – 273• 26) 443 K• 41) 1 hour/60 min b) 103mg/1g c) 103mL/1dm3

• 42) 1.48 x 107 micrograms b) 3.72 g c) 6.63 x 104 cm3

Practice problems

• How many:– Meters in a kilometer?– Centigrams in a gram?– Milliliters in a liter?– Microkelvins in a kelvin?– Joules in a Megajoule?– Nanometers in a meter?– Moles in a hectomole?

Conversion Problems

• A quantity can usually be expressed in several different ways– 1 dollar = 4 quarters = 10 dimes = 20 nickels

• The same is true of scientific quantities– 1 meter = 10 decimeters = 100 centimeters

• How do we convert from one unit to another?

Conversion problems

• How do we convert from one unit to another?– Conversion factors

• A conversion factor is a ratio of equivalent measurements used to convert one unit to another. – Example: 1 meter (m) = 100 centimeters (cm)

Convert 2 m to cm2 m x = 200 cm

Conversion problems

• How do I choose a conversion factor?– Find an equivalency between the unit your

measurement is in and the unit you’re changing to– Set up a ratio of equivalent measurements– Place your desired unit on top

Converting 760 grams to kilograms1000 g = 1 kg760 g x = = 0.76 kg

Practice problems

• Convert using conversion factors:1) 750 milliliters to liters2) 15 centimeters to meters3) 1.5 decimeters to meters4) 750 kilojoules to Megajoules5) 5 nanograms to grams6) 4.5 kilokelvins to centikelvins

Dimensional AnalysisSolve the following problems with conversion factors:• How many seconds are in 8 hours?

• How many inches are in a mile?

• How many Joules are in 200 calories?

Density

• Use your intuition– What is more dense, a bucket of pennies or a

bucket of feathers?

– What is more dense, a block of wood or a block of iron?

– What does density mean?

Density

• What is density?– Density is the ratio of an object’s mass to it’s

volume• Density =

– Stated another way, density is a measure of how tightly matter is packed in an object

Practice problem

• You have four blocks of different elements. Use a ruler and a balance to calculate the density of each.

Buoyancy

• Density determines whether an object will sink or float in a fluid. – More dense sink– Less dense float

• Is wood more or less dense than water?• Is a rock more or less dense than water?• Is a person more or less dense than water?