Measurements

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MEASUREMENTA 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 unitGrams

Tool to measure mass? Digital balance

VOLUME INDICATES AN AMOUNT OF SPACE.

VOLUME

Base unit Liters

Tool used to measure volume? Graduated cylinder

1 mL = 1 cm3

You can measure the volume of a liquid using a graduated cylinder.

VOLUME

THINK ABOUT THIS…

Does an egg size piece of steel or wood have the same mass?

3 blocks of equal volume

3 different mass values

plastic glass iron

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

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?

Density

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:

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.

45 1.0

m g mLV

d g cm cmmL

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 has volume

AIR IS MATTER!

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?

REVIEW OF MEASUREMENTS

Is the mass exactly 10.0 g?

We don’t know since any mass between 9.95 g and 10.05 g would round off to 10.0 g

Could it be 9.96 g? 10.04 g?

10.0 ± 0.1g

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

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.

What value should be recorded for the volume measurement in the picture?

PRECISION AND ACCURACY

Science encompasses very large and very small objects.

We use a shorthand numerical method to write large or small numbers…

Large Small

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

mantissa

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

= 3.6 x 103

83,100

= 8.31 x 104

Scientific notation

Convert 0.00065 to scientific notation.

Scientific notation

Asked: The number in scientific notation

Given: 0.00065 as a decimal number

Relationships:

Answer:

40.0001 1046.5 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

Using scientific notation on a calculator

Scientific notation

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

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

In Summary

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?

hypothesis: a tentative explanation for something, or a tentative answer to a question.

“I think sugar dissolves

faster in hot water.”

a hypothesis!

Does sugar dissolve faster in hot water?

experiment: a situation specially set up to observe how something happens or to test a hypothesis.

Testing a hypothesis requires scientific evidence from experiments.

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.

What could affect dissolving?

• Water temperature• Amount of sugar• Amount of water

Variables

We don’t know if our hypothesis is correct because more than one variable changed at the same time!

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

IN EVERY EXPERIMENT THERE IS ALWAYS SOME UNCERTAINTY AND ERROR

You can do this water and sugar experiment 3 times, follow the exact same steps, and yet still come up with three slightly different resultsWhy do you think that may be the case?

ERROR IS NOT A MISTAKE

Error:

The unavoidable difference between the real measurement and the true value of what you are measuring

TAKE THE AVERAGE

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???

Why take the average?

• To improve accuracy

• Comparing the actual measurement

with the average gives you an

estimate of the error

How can we know the error if we don’t know the true value?Assume the average is the true value.

Accuracy

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

Measurements

Education