what is measurement? units of measurement when do you measure? measure your height. read your...
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What is measurement? Units of
Measurement When do you
Measure?• measure your height. • read your watch.• take your temperature.
• weigh a cantaloupe.
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Measurement in ChemistryIn chemistry we
• measure quantities.• do experiments.• calculate results. • use numbers to report
measurements.• compare results to
standards.• all with needed tools• every measurement,
• number followed by unit
Number and Unit
35 m
0.25 L
225 lb
3.4 hr
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The Metric System (SI)
metric system or SI (international system)
• decimal system based on 10.
• Used worldwide.(M)
• Used by scientists (SI).
following unit used for each type of measurement:
Measurement Metric SILength
meter (m) meter (m)Volume
liter (L) cubic meter (m3)Mass
gram (g) kilogram (kg)Time
second (s) second (s)Temperature
Celsius (C) Kelvin (K)
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Length Measurement
Length
• measured using a meter stick.
• Uses unit of meter (m) in both systems.
• unit of an inch equal to exactly 2.54 centimeters in metric (SI) system.
1 in. = 2.54 cm
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Volume Measurement
Volume • space occupied by a
substance. • measured using a
graduated cylinder (liquids)
• metric system• unit liter (L) in• 1 L = 1.057 qt
• SI system (solids)• m3(cubic meter)
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Mass Measurement
mass of an object
• quantity of material it contains.
• measured • balance.
• metric system• . gram (g)
• SI system• kilogram (kg)
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
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Temperature Measurement
temperature of a substance • indicates how hot or cold.• metric system
• Celsius (C)
• SI system • Kelvin (K) scale.
• thermometer here shows• 18ºC or 64ºF.
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Time Measurement
Time measurement
• metric and SI systems.• second(s)
• based on an atomic clock • uses a frequency
emitted by cesium atoms
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What are scientific notation?• very large or very small numbers
• coefficient and a power of 10• width human hair is 0.000 008 m
• written 8 x 10-6 m.• large number such as 4 500 000 s
• written 4.5 x 106 s
• Let’s explore more ! coefficient power of ten coefficient
power of ten 1.5 x 102 7.35 x
10-4
decimal point moved after first digit
spaces moved shown as power of ten. 52 000. = 5.2 x 10 4 0.00378 = 3.78 x
10-3
4 spaces left 3 spaces right
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Some Powers of Ten
Numbers written in standard format
and in scientific notation.
Diameter of the Earth12 800 000 m
1.28 x 107 m Mass of a human
68 kg 6.8 x 101 kg
Length of a pox virus0.000 03 cm
3 x 10-5 cm10
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. l2. . . . l . . . . l3 . . . . l . . . . l4. . cm
• determine a quantity such as height or mass• markings on meter stick end of orange line are read
asfirst digit 2 plus second digit 2.7
• last digit obtained by estimating• length reported as 2.76 cmdigits 2 and 7 are certain
(known).• The final digit 6 was estimated (uncertain).• All three digits (2.76) are significant including
estimated digit.
What are measured numbers ?
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. l3. . . . l . . . . l4. . . . l . . . . l5. . cm
• For this measurement• first and second known digits are 4.5.
• line ends on mark• estimated digit in hundredths place 0.
• measurement • reported as 4.50 cm.
Zero as a Measured Number!
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What are significant numbers?Significant figures • obtained from
measurement• include all known
digits plus estimated digit.
• reported • measurement depend on
measuring tool.
• non-zero numbers in measured number are significant.
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38.15 cm 45.6 ft 265.6 lb
3122.55 m 5
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The two kinds of zeros?
Sandwiched zeros• occur between nonzero
numbers.• are significant.
Number significant digits
50.8 mm 32001 min 4 0.0702 lb 3 0.40505 m 5
Trailing zeros & Leading zeros
• follow non-zero numbers in numbers without decimal points.
• Precede non-zero digits in a decimal number
• are usually place holders. • are not significant.
Number significant digits
25 000 cm 2 200 kg 10.0156 oz 30.0042 lb 225 005 000 g 5
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What are prefixes?
A prefixfront of a unit increases or decreases size makes units larger or smaller
one or more factors of 10. indicates a numerical value.
prefix = value1 kilometer = 1000 meters
1 kilogram = 1000 grams
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Metric and SI Prefixes need to know!
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An equality
states same measurement in two different units.can be written using
relationships between two metric units.
Example: 1 meter same as 100 cm and 1000 mm.
1 m = 100 cm1 m = 1000 mm
What are metric equalities?
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Measuring Length
Several equalities can be written for length metric (SI) system
1 km = 1000 m
1 m = 1000 mm
1 m = 100 cm
1 mm = 0.001 m
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Measuring Volume
Several equalities can bewritten for volume metric(SI) system
1 kl = 1000 l1 l = 1000 ml1 l = 100 cl1 ml = 0.001 l
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Measuring Mass
Several equalities can be
written for mass metric (SI) system
1 kg = 1000 g1 g = 1000 mg1 g = 100 cg
1 mg = 0.001 g
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Equalities • use two different units
• Describe same measured amount.
• written for relationships between units of the metric system, U.S. units, or between
For example,
1 m = 1000 mm
1 lb = 16 oz
2.205 lb = 1 kg
Other equalities between metric and U.S. units?
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Some Common Equalities
contents of packaged foods
• U.S. are listed as both metric and U.S. units• Indicate same amount of a substance in two
different units.
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A conversion factor • fraction obtained from an equality
Equality: 1 in. = 2.54 cm• written as a ratio with a numerator and
denominator.
• can be inverted to give two conversion factors for every equality. 1 in. and 2.54 cm
2.54 cm 1 in.
Use conversion factors to change between units!
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A conversion factor • may be obtained from information in a word
problem.• written for that problem only.
Example 1: The price of one pound (1 lb) of red peppers is
$2.39.1 lb red peppers and $2.39$2.39 1 lb red peppers
Example 2: The cost of one gallon (1 gal) of gas is $2.34.
1 gallon of gas and $2.34$2.34 1 gallon of gas
Conversion Factors in a Problem
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A percent factor• Gives ratio of the parts to whole.
% = Parts x 100Whole
• Uses same unit to express percent.• Uses value 100 and unit for whole.• can be written as two factors.
Example: A food contains 30% (by mass) fat.
30 g fat and 100 g food100 g food 30 g fat
Percent as a Conversion Factor
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The thickness of the skin fold at
the waist indicates 11% body
fat. What percent factors can be
written for body fat in kg?
Percent factors using kg:
11 kg fat and 100 kg mass
100 kg mass 11 kg fat
Another example!
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To solve a problem• Identify given unit• Identify needed unit.
Example: A person has a height of 2.0 meters. What is that height in inches?
given unit is initial unit of height. given unit = meters (m)
needed unit is unit for answer. needed unit = inches (in.)
Given and Needed Units can be used in problem solving!
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Learning Check
An injured person loses 0.30 pints of blood. How
many milliliters of blood would that be?
Identify the given and needed units given in this
problem.
Given unit = _______
Needed unit = _______
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1. Write given and needed units.2. Write a unit plan to convert given unit to needed
unit.3. Write equalities and conversion factors to
connect units.4. Use conversion factors to cancel given unit and
provide needed unit.
Unit 1 x Unit 2 = Unit 2
Unit 1Given x Conversion = Needed
unit factor unit
Problem Setup steps!
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How many minutes are 2.5 hours?
Given unit = 2.5 hrNeeded unit = minUnit Plan = hr
min
Setup problem to cancel hours (hr).
Given Conversion Neededunit factor unit2.5 hr x 60 min = 150 min
(2 SF) 1 hr
Setting up a Problem
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
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A rattlesnake is 2.44 m long. How many centimeters long is the snake?
Given Conversion Neededunit factor unit
2.44 m x 100 cm = 244 cm 1 m
A solved example
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• Often, two or more conversion factors are required to obtain unit needed for answer.Unit 1 Unit 2Unit 3
• Additional conversion factors are placed in setup to cancel each preceding unit
Given unit x factor 1 x factor 2 = needed unitUnit 1 x Unit 2 x Unit 3 = Unit 3
Unit 1 Unit 2
Using Two or More Factors
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How many minutes are in 1.4 days? Given unit: 1.4 days
Factor 1 Factor 2 Plan: days hr min
Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 103 min
1 day 1 hr 2 SF Exact Exact = 2 SF
Example: Problem Solving
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• check your unit cancellation in setup.• units in conversion factors must cancel to give
correct unit for answer.
What is wrong with the following setup?
1.4 day x 1 day x 1 hr 24 hr 60 min
Units = day2/min is not the unit neededUnits don’t cancel properly.
Remember to check the unit cancellation!
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Another example! the GPS
What is 165 lb in kg?STEP 1 Given 165 lb Need
kgSTEP 2 PlanSTEP 3 Equalities/Factors 1 kg = 2.20 lb 2.20 lb and 1 kg
1 kg 2.20 lbSTEP 4 Set Up Problem 165 lb x 1 kg = 75.0
kg 2.20 lb
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Given: 4.65 L Needed: gallons
Plan: L qt gallon
Equalities: 1.06 qt = 1 L; 1 gal = 4 qt
Set Up Problem:
4.65 L x x 1.06 qt x 1 gal = 1.23 gal 1 L 4 qt
3 SF 3 SF exact 3 SF
A bucket contains 4.65 L of water. How many gallons of water is that?
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3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm
Calculator answer: 914.4 mm Needed answer: 910 mm (2 SF rounded)
Check factor setup: Units cancel properlyCheck needed unit: mm
If a ski pole is 3.0 feet in length, how long is the ski pole in mm?
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If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet?
Given: 7500 ft 65 m/min Need: min
Plan: ft in. cm m min
Equalities: 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm
1 min = 65 m (walking pace)
Set Up Problem:
7500 ft x 12 in. x 2.54 cm x 1m x 1 min 1 ft 1 in. 100 cm 65 m
= 35 min final answer (2 SF)
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Percent Factor in a Problem
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg?
percent factor
86 kg mass x 11 kg fat
100 kg mass
= 9.5 kg fat
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Another example:
How many lb of sugar are in 120 g of candy if the candy is 25%(by mass) sugar?
percent factor
120 g candy x 1 lb candy x 25 lb sugar
454 g candy 100 lb candy
= 0.066 lb sugar
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Density• Compares the mass of an object to its
volume.• Is the mass of a substance divided by its
volume.
Density expressionDensity = mass = g or g = g/cm3 volume mL cm3
Note: 1 mL = 1 cm3
• Ice floats in water • because density of ice is less than density of
water.
• Aluminum sinks • because its density is greater than density of
water
What is density?
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Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?
Given: mass = 50.0 g volume = 22.2 cm3
Plan: Place the mass and volume of the osmium metal
in the density expression.
D = mass = 50.0 g volume 2.22 cm3
calculator = 22.522522 g/cm3
final answer (2) = 22.5 g/cm3
Problem on density
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How to determine volume by displacement ?
• solid completely submerged in water displaces its own volume of water.
• volume of solid is calculated from volume difference.45.0 mL - 35.5 mL
= 9.5 mL = 9.5 cm3
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Density Using Volume Displacement
The density of the zinc object is
then calculated from its mass
and volume.
mass = 68.60 g = 7.2 g/cm3 volume 9.5 cm3
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What is the density (g/cm3) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?
Find the volume first?
object
33.0 mL 25.0 mL
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Solution
Given: 48.0 g Volume of water = 25.0 mL
Volume of water + metal = 33.0 mL
Need: Density (g/mL)Plan: Calculate the volume difference. Change to
cm3, and place in density expression.
33.0 mL - 25.0 mL = 8.0 mL
8.0 mL x 1 cm3 = 8.0 cm3
1 mLSet up Problem:
Density = 48.0 g = 6.0 g = 6.0 g/cm3
8.0 cm3 1 cm3