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MEASUREMENT 
A very useful skill
IMPORTANT CONCEPTS AND SKILLS TO BE 
LEARNED 
 Scientific Method Application 
 Graphing Skills 
 Variables- experimental or control 
 Dimensional Analysis and Conversions 
 Uncertainty in measurements 
 Use of basic lab equipment and measurements
MEASUREMENT 
 Information that describes a physical quantity with 
both a number and a unit. 
 What type of measurements can you make from the 
picture below?
YOU ARE RESPONSIBLE FOR KNOWING… 
1. The base units for each type of measurement 
2. The specific tools used in the lab to make the 
measurements 
3. Converting from the base unit to others 
for example Grams to kilograms
USING CLEAR STANDARDS OF MEASUREMENTS, WE CAN 
COMMUNICATE MORE EFFECTIVELY 
IN ANSWERING SIMPLE QUESTIONS. 
 How heavy is an egg? 
 How much space does an 
egg occupy? 
 Does an egg size piece of 
steel or 
wood have the same mass? 
 How hard is it to crush an 
egg by squeezing 
evenly from all sides?
MASS VS. WEIGHT 
 Mass ( How heavy is an egg?) 
How much matter is present in an object 
 Weight 
The force of gravity 
Weight = Mass x Gravity
MASS VS. WEIGHT 
Base unit 
Grams 
Tool to measure mass? 
Digital balance
VOLUME INDICATES AN AMOUNT OF 
SPACE.
VOLUME 
Base unit 
Liters 
Tool used to measure volume? 
Graduated cylinder
You can measure the volume of a 
liquid using a graduated cylinder. 
VOLUME 
1 mL = 1 cm3
THINK ABOUT THIS… 
 Does an egg size piece of 
steel or wood have the same 
mass?
3 blocks of equal volume 
plastic glass iron 
3 different mass values 
DENSITY
DENSITY 
 How much mass is in a given volume of material 
 EQUAL SIZE DOES NOT MEAN EQUAL MASS 
 Density is a CALCULATED measurement
RELATIONSHIP BETWEEN MASS AND VOLUME
Density 
If 45 g of titanium are added to a graduated cylinder containing 50 mL 
of water, what will the cylinder read after the titanium has been added? 
Asked: Volume of graduated cylinder after adding 45 g of titanium 
Given: 45 g of titanium, density of titanium d = 4.5 g/cm3, 50 mL of water 
Relationships: 
Solve: 
d m 
V 
 
45 1.0 
    mL 
The titanium adds 10 mL to the cylinder, which now reads 60 mL. 
Answer: 60 mL 
Discussion: This is an example of measurement using the displacement 
method. 
3 3 
4 
0 
.5 
1 
m g mL 
V 
d g cm cm
GET YOUR CALCULATORS OUT! 
 1. Calculate the density of 100 g of lead (Pb) that 
occupies a volume of 8.80 cm3. 
 2. Calculate the density of 100 g of water (H2O) that 
occupies a volume of 100 cm3. 
 3. A gold bracelet has a mass of 46.23g. The 
density of gold (Au) is 19.3 g/cm3. Calculate the 
volume of this bracelet.
PRESSURE 
 How hard is it to crush an egg by 
squeezing 
evenly from all sides?
PRESSURE 
 Force per unit area exerted by matter, acts equally 
in all directions within a liquid or a gas. 
 Base units of Pressure 
Pascal Pa (N/m2) 
Pounds per Square Inch psi (lb/in2) 
Atmosphere atm
Is an empty bottle 
full of nothing? 
Can you squeeze a bottle 
that is tightly capped? 
Does air have pressure?
Air has mass 
Air has 
pressure 
AIR IS MATTER! 
Air has volume
REVIEW OF MEASUREMENTS 
Mass 
How heavy is an egg? 
Volume 
How much space does an egg occupy? 
Density 
Does an egg size piece of steel or 
wood have the same mass? 
Pressure 
How hard is it to crush an egg by squeezing 
evenly from all sides?
ACCURACY AND PRECISION 
Is the mass exactly 10.0 g? 
10.0 ± 0.1g 
Could it be 9.96 g? 
10.04 g? 
We don’t know since any mass between 9.95 g and 10.05 g 
would round off to 10.0 g
ACCURACY AND PRECISION 
Accuracy 
A term that 
describes how 
close a 
measurement 
is to the true 
value 
 Precision 
A term that 
describes how 
close 
measured 
values are to 
each other
ACCURACY AND PRECISION
SIGNIFICANT FIGURES 
 A digit that represents an actual measurement 
 used to convey the precision of measurements 
without having to write ± after each value 
 In this class 
we will round the measurements 
off to two decimal places
PRECISION AND ACCURACY 
What value should be recorded for the volume 
measurement in the picture? 
Asked: The value with the correct number 
of significant figures 
Given: You can estimate to a tenth of the 
graduation of a cylinder or ruler 
Relationships: The last digit on the right is assumed to be plus or minus 
one-tenth. 
Solve: The meniscus is right on 18, so estimate 18.0 mL. 
Answer: 18.0 mL 
Discussion: The real value is confidently known to be between 17.9 
and 18.1 mL.
Science encompasses very large and very small objects. 
Large Small 
We use a shorthand numerical method to write 
large or small numbers…
SCIENTIFIC NOTATION 
 A method of writing 
numbers as a base 
times the power of ten 
 Mantissa 
the first number 
 Power of ten 
The second number 
with exponent 
mantissa 
 1,500 = 15 x 100 
power of 10 
= 102 
exponent
1,500 in scientific notation: 1.5 x 103 
1,500 = 1.5 x 1,000 
= 103 
mantissa 
Scientific notation
Scientific notation 
0.000 000 4 
= 4 x 10–7 
0.003 6 
= 3.6 x 10–3 
0.000 083 1 
= 8.31 x 10–5
Scientific notation 
40,000,000 
= 4 x 107 
3,600 
= 3.6 x 103 
83,100 
= 8.31 x 104
Convert 0.00065 to scientific notation. 
Scientific notation 
Asked: The number in scientific notation 
Given: 0.00065 as a decimal number 
Relationships: 
0.0001  
10 4 Answer: 
4 6.5 10 
YOUR TURN 
 Practice moving the decimal point in the correct 
direction. Take the following numbers out of scientific 
notation, and write them out showing the correct number 
of zeros. 
a. 9 × 106 _9,000,000__ 
b. 3.7 × 10–3 _0.0037__ 
c. 3.56 × 103__3,560__ 
d. 2.14 × 10–7_0.000000214
PRACTICE IS GOOD FOR YOU 
2. Write the following numbers in scientific notation. 
 a. 62,100 __6.21 × 104 
 b. 0.00521 _5.21 × 10–3 
 c. 5050 __5.05 × 103 
 d. 0.000000717 __7.17 × 10–7
Scientific notation 
Using scientific notation on a calculator
CONVERSIONS 
 You need to be able to translate between different 
units of measurements…. DIMENSIONAL 
ANALYSIS 
 Conversion factors help you do this task! 
 Conversion factor : a ratio of two different units 
that has a value of 1 
Example 12 eggs / 1 dozen 
12 inches / 1 foot
In Summary 
Measuring physical properties 
Mass grams 
Volume liters 
Density grams per liter 
Pressure atmospheres, psi 
Precision vs. accuracy 
Scientific notation 
40,000,000 
= 4 x 107 
0.000 000 4 
= 4 x 10–7
The universe obeys a set of unwritten rules… 
… called natural laws.
How can we approach these 
questions? 
Questions 
Evidence 
Theory
SCIENTIFIC METHOD INVOLVES… 
 Inquiry : the process 
of learning through 
asking questions 
 Theory : an 
explanation that is 
supported by evidence
Does sugar dissolve 
faster in hot water? 
Can you make an educated guess? 
What is another term we 
use in science for 
educated guess?
Does sugar dissolve 
faster in hot water? 
“I think sugar 
dissolves faster 
in hot water.” 
a hypothesis! 
hypothesis: a tentative explanation for something, or 
a tentative answer to a question.
Testing a hypothesis 
requires scientific 
evidence from 
experiments. 
experiment: a situation specially set up to observe how 
something happens or to test a hypothesis.
VARIABLES 
 Experimental variable 
The single variable that is changed to test its effect 
 Control Variables 
The variables that are kept constant during the 
experiment
Objective observation: 
The time it takes the sugar to dissolve changes in each trial.
One experimental setup: 
Does this support our hypothesis? YES NO MAYBE 
“I think sugar 
dissolves faster 
in hot water.”
One experimental setup: 
What could affect dissolving? 
• Water temperature 
• Amount of sugar 
• Amount of water 
Variables
variable: a quantity that is measured or changed in an 
experiment or observation. 
We don’t know if our hypothesis is correct because 
more than one variable changed at the same time! 
What could affect dissolving? 
• Water temperature 
• Amount of sugar 
• Amount of water 
Variables
TYPES OF VARIABLES 
 Experimental Variable: 
The single variable that is changed to test its effect 
 Control Variables: 
Variables that are kept constant during an experiment
 You can do this water and sugar 
experiment 3 times, 
follow the exact same steps, 
and yet still come up with 
three slightly different results 
Why do you think that may be the case? 
IN EVERY EXPERIMENT THERE 
IS ALWAYS SOME UNCERTAINTY 
AND ERROR
ERROR IS NOT A MISTAKE 
Error: 
The unavoidable difference 
between the real measurement 
and the true value of what you are measuring
 So when you take many measurements of the same 
test… 
what would you do to help make an educated 
guess 
as to what the value may actually be??? 
TAKE THE AVERAGE
Why take the average? 
• To improve accuracy 
• Comparing the actual measurement 
with the average gives you an 
estimate of the error
Accuracy 
How can we know the error if we don’t know the true value? 
Assume the average is the true value.
WHAT DO WE DO WITH THE DATA COLLECTED? 
 DRAW CONCLUSIONS 
A stated decision whether or not the results of the 
experiments or observations confirm an idea or 
hypothesis

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Measurements

  • 1. MEASUREMENT A very useful skill
  • 2. IMPORTANT CONCEPTS AND SKILLS TO BE LEARNED  Scientific Method Application  Graphing Skills  Variables- experimental or control  Dimensional Analysis and Conversions  Uncertainty in measurements  Use of basic lab equipment and measurements
  • 3. MEASUREMENT  Information that describes a physical quantity with both a number and a unit.  What type of measurements can you make from the picture below?
  • 4. YOU ARE RESPONSIBLE FOR KNOWING… 1. The base units for each type of measurement 2. The specific tools used in the lab to make the measurements 3. Converting from the base unit to others for example Grams to kilograms
  • 5. USING CLEAR STANDARDS OF MEASUREMENTS, WE CAN COMMUNICATE MORE EFFECTIVELY IN ANSWERING SIMPLE QUESTIONS.  How heavy is an egg?  How much space does an egg occupy?  Does an egg size piece of steel or wood have the same mass?  How hard is it to crush an egg by squeezing evenly from all sides?
  • 6. MASS VS. WEIGHT  Mass ( How heavy is an egg?) How much matter is present in an object  Weight The force of gravity Weight = Mass x Gravity
  • 7. MASS VS. WEIGHT Base unit Grams Tool to measure mass? Digital balance
  • 8. VOLUME INDICATES AN AMOUNT OF SPACE.
  • 9. VOLUME Base unit Liters Tool used to measure volume? Graduated cylinder
  • 10. You can measure the volume of a liquid using a graduated cylinder. VOLUME 1 mL = 1 cm3
  • 11. THINK ABOUT THIS…  Does an egg size piece of steel or wood have the same mass?
  • 12. 3 blocks of equal volume plastic glass iron 3 different mass values DENSITY
  • 13. DENSITY  How much mass is in a given volume of material  EQUAL SIZE DOES NOT MEAN EQUAL MASS  Density is a CALCULATED measurement
  • 15. Density If 45 g of titanium are added to a graduated cylinder containing 50 mL of water, what will the cylinder read after the titanium has been added? Asked: Volume of graduated cylinder after adding 45 g of titanium Given: 45 g of titanium, density of titanium d = 4.5 g/cm3, 50 mL of water Relationships: Solve: d m V  45 1.0     mL The titanium adds 10 mL to the cylinder, which now reads 60 mL. Answer: 60 mL Discussion: This is an example of measurement using the displacement method. 3 3 4 0 .5 1 m g mL V d g cm cm
  • 16. GET YOUR CALCULATORS OUT!  1. Calculate the density of 100 g of lead (Pb) that occupies a volume of 8.80 cm3.  2. Calculate the density of 100 g of water (H2O) that occupies a volume of 100 cm3.  3. A gold bracelet has a mass of 46.23g. The density of gold (Au) is 19.3 g/cm3. Calculate the volume of this bracelet.
  • 17. PRESSURE  How hard is it to crush an egg by squeezing evenly from all sides?
  • 18.
  • 19. PRESSURE  Force per unit area exerted by matter, acts equally in all directions within a liquid or a gas.  Base units of Pressure Pascal Pa (N/m2) Pounds per Square Inch psi (lb/in2) Atmosphere atm
  • 20. Is an empty bottle full of nothing? Can you squeeze a bottle that is tightly capped? Does air have pressure?
  • 21. Air has mass Air has pressure AIR IS MATTER! Air has volume
  • 22. REVIEW OF MEASUREMENTS Mass How heavy is an egg? Volume How much space does an egg occupy? Density Does an egg size piece of steel or wood have the same mass? Pressure How hard is it to crush an egg by squeezing evenly from all sides?
  • 23. ACCURACY AND PRECISION Is the mass exactly 10.0 g? 10.0 ± 0.1g Could it be 9.96 g? 10.04 g? We don’t know since any mass between 9.95 g and 10.05 g would round off to 10.0 g
  • 24. ACCURACY AND PRECISION Accuracy A term that describes how close a measurement is to the true value  Precision A term that describes how close measured values are to each other
  • 26. SIGNIFICANT FIGURES  A digit that represents an actual measurement  used to convey the precision of measurements without having to write ± after each value  In this class we will round the measurements off to two decimal places
  • 27. PRECISION AND ACCURACY What value should be recorded for the volume measurement in the picture? Asked: The value with the correct number of significant figures Given: You can estimate to a tenth of the graduation of a cylinder or ruler Relationships: The last digit on the right is assumed to be plus or minus one-tenth. Solve: The meniscus is right on 18, so estimate 18.0 mL. Answer: 18.0 mL Discussion: The real value is confidently known to be between 17.9 and 18.1 mL.
  • 28. Science encompasses very large and very small objects. Large Small We use a shorthand numerical method to write large or small numbers…
  • 29. SCIENTIFIC NOTATION  A method of writing numbers as a base times the power of ten  Mantissa the first number  Power of ten The second number with exponent mantissa  1,500 = 15 x 100 power of 10 = 102 exponent
  • 30. 1,500 in scientific notation: 1.5 x 103 1,500 = 1.5 x 1,000 = 103 mantissa Scientific notation
  • 31. Scientific notation 0.000 000 4 = 4 x 10–7 0.003 6 = 3.6 x 10–3 0.000 083 1 = 8.31 x 10–5
  • 32. Scientific notation 40,000,000 = 4 x 107 3,600 = 3.6 x 103 83,100 = 8.31 x 104
  • 33. Convert 0.00065 to scientific notation. Scientific notation Asked: The number in scientific notation Given: 0.00065 as a decimal number Relationships: 0.0001  10 4 Answer: 4 6.5 10 
  • 34. YOUR TURN  Practice moving the decimal point in the correct direction. Take the following numbers out of scientific notation, and write them out showing the correct number of zeros. a. 9 × 106 _9,000,000__ b. 3.7 × 10–3 _0.0037__ c. 3.56 × 103__3,560__ d. 2.14 × 10–7_0.000000214
  • 35. PRACTICE IS GOOD FOR YOU 2. Write the following numbers in scientific notation.  a. 62,100 __6.21 × 104  b. 0.00521 _5.21 × 10–3  c. 5050 __5.05 × 103  d. 0.000000717 __7.17 × 10–7
  • 36. Scientific notation Using scientific notation on a calculator
  • 37. CONVERSIONS  You need to be able to translate between different units of measurements…. DIMENSIONAL ANALYSIS  Conversion factors help you do this task!  Conversion factor : a ratio of two different units that has a value of 1 Example 12 eggs / 1 dozen 12 inches / 1 foot
  • 38. In Summary Measuring physical properties Mass grams Volume liters Density grams per liter Pressure atmospheres, psi Precision vs. accuracy Scientific notation 40,000,000 = 4 x 107 0.000 000 4 = 4 x 10–7
  • 39. The universe obeys a set of unwritten rules… … called natural laws.
  • 40. How can we approach these questions? Questions Evidence Theory
  • 41. SCIENTIFIC METHOD INVOLVES…  Inquiry : the process of learning through asking questions  Theory : an explanation that is supported by evidence
  • 42. Does sugar dissolve faster in hot water? Can you make an educated guess? What is another term we use in science for educated guess?
  • 43. Does sugar dissolve faster in hot water? “I think sugar dissolves faster in hot water.” a hypothesis! hypothesis: a tentative explanation for something, or a tentative answer to a question.
  • 44. Testing a hypothesis requires scientific evidence from experiments. experiment: a situation specially set up to observe how something happens or to test a hypothesis.
  • 45. VARIABLES  Experimental variable The single variable that is changed to test its effect  Control Variables The variables that are kept constant during the experiment
  • 46. Objective observation: The time it takes the sugar to dissolve changes in each trial.
  • 47. One experimental setup: Does this support our hypothesis? YES NO MAYBE “I think sugar dissolves faster in hot water.”
  • 48. One experimental setup: What could affect dissolving? • Water temperature • Amount of sugar • Amount of water Variables
  • 49. variable: a quantity that is measured or changed in an experiment or observation. We don’t know if our hypothesis is correct because more than one variable changed at the same time! What could affect dissolving? • Water temperature • Amount of sugar • Amount of water Variables
  • 50. TYPES OF VARIABLES  Experimental Variable: The single variable that is changed to test its effect  Control Variables: Variables that are kept constant during an experiment
  • 51.  You can do this water and sugar experiment 3 times, follow the exact same steps, and yet still come up with three slightly different results Why do you think that may be the case? IN EVERY EXPERIMENT THERE IS ALWAYS SOME UNCERTAINTY AND ERROR
  • 52. ERROR IS NOT A MISTAKE Error: The unavoidable difference between the real measurement and the true value of what you are measuring
  • 53.  So when you take many measurements of the same test… what would you do to help make an educated guess as to what the value may actually be??? TAKE THE AVERAGE
  • 54. Why take the average? • To improve accuracy • Comparing the actual measurement with the average gives you an estimate of the error
  • 55. Accuracy How can we know the error if we don’t know the true value? Assume the average is the true value.
  • 56. WHAT DO WE DO WITH THE DATA COLLECTED?  DRAW CONCLUSIONS A stated decision whether or not the results of the experiments or observations confirm an idea or hypothesis