DensityDensity

What is it and how do we use it?What is it and how do we use it?

DensityDensity

Density is a ratio that compares the mass of an Density is a ratio that compares the mass of an object to its volume.object to its volume.

Density can be found using the formula:Density can be found using the formula:

Density = Density = MassMass

VolumeVolume

ProblemsProblems

1.1. A piece of metal with a mass of 147 g is A piece of metal with a mass of 147 g is placed in a 50-mL graduated cylinder. The placed in a 50-mL graduated cylinder. The water level rises from 20 mL to 41 mL. water level rises from 20 mL to 41 mL. What is the density of the metal?What is the density of the metal?

2.2. What is the volume of a sample that has a What is the volume of a sample that has a mass of 20 g and a density of 4 g/mL?mass of 20 g and a density of 4 g/mL?

3.3. A metal cube has a mass of 20 g and a A metal cube has a mass of 20 g and a volume of 5 cm³. Is the cube made of pure volume of 5 cm³. Is the cube made of pure aluminum? Explain your answer.aluminum? Explain your answer.

AnswersAnswers

1.1. 7.0 g/mL7.0 g/mL

2.2. 5 mL5 mL

3.3. No; the density of aluminum is 2.7 g/cm³; the No; the density of aluminum is 2.7 g/cm³; the density of the cube is 4 g/cm³.density of the cube is 4 g/cm³.

TemperatureTemperature

What scale to use?What scale to use?

Measuring TemperatureMeasuring Temperature A A thermometerthermometer is an instrument that is an instrument that

measures temperature, or how hot an object measures temperature, or how hot an object is. is.

The two temperature scales that you are The two temperature scales that you are probably most familiar with are the probably most familiar with are the Fahrenheit scale and the Celsius scale Fahrenheit scale and the Celsius scale

You can convert from one scale to the other You can convert from one scale to the other by using one of the following formulas. by using one of the following formulas.

The Kelvin ScaleThe Kelvin Scale

The The kelvinkelvin is the SI unit of temperature. is the SI unit of temperature. On the Kelvin scale, water freezes ar about On the Kelvin scale, water freezes ar about

273 K and boils at 373 K.273 K and boils at 373 K. It is easy to convert from celsius to kelvin.It is easy to convert from celsius to kelvin.

Kelvin = °C + 273Kelvin = °C + 273 No degree sign is needed with kelvin.No degree sign is needed with kelvin.

Operations with Operations with Scientific NotationScientific Notation

Adding and SubtractingAdding and SubtractingMultiplying and DividingMultiplying and Dividing

Adding and SubtractingAdding and Subtracting

1.1. Exponents must be the same or the operation Exponents must be the same or the operation cannotcannot be performed. If the exponents do be performed. If the exponents do not agree, change the decimal and the power not agree, change the decimal and the power of ten notation of either number so as to of ten notation of either number so as to agree with the other.agree with the other.

2.2. Add or subtract the number.Add or subtract the number.

3.3. Keep the same power of ten.Keep the same power of ten.

Multiplying and DividingMultiplying and Dividing

MULTIPLICATION:MULTIPLICATION:

1.1. Multiply the numbers.Multiply the numbers.

2.2. Add the exponents for the power of ten.Add the exponents for the power of ten.

DIVISION:DIVISION:

1.1. Divide the numbers as in any division problem.Divide the numbers as in any division problem.

2.2. Subtract the denominator power of ten exponent Subtract the denominator power of ten exponent from the numerator power of ten exponent.from the numerator power of ten exponent.

Percent ErrorPercent Error

How much uncertainty?How much uncertainty?

Percent ErrorPercent Error

Percent error is used to calculate the accuracy Percent error is used to calculate the accuracy of experimental data values and the accepted of experimental data values and the accepted value.value.

Percent errorPercent error is the ratio of an error to its is the ratio of an error to its accepted value and can be found using the accepted value and can be found using the following formula:following formula:

Percent error = Percent error = error . error . X 100 X 100

accepted valueaccepted value

Significant FiguresSignificant Figures

What are they?What are they?

Significant figuresSignificant figures

Scientists indicate the precision of a Scientists indicate the precision of a measurement by the number of digits they measurement by the number of digits they report.report.

3.52 g is more precise than 3.5 g.3.52 g is more precise than 3.5 g. The digits they report are called significant The digits they report are called significant

figures.figures. Significant figuresSignificant figures include all known digits include all known digits

plus one estimated digit. plus one estimated digit.

Rules for Significant FiguresRules for Significant Figures

1.1. All non-zero numbers are always significant.All non-zero numbers are always significant.2.2. Zeros between non-zero numbers are always Zeros between non-zero numbers are always

significant.significant.3.3. All final zeros to the right of the decimal All final zeros to the right of the decimal

place are significant.place are significant.4.4. Zeros that act as placeholders are not Zeros that act as placeholders are not

significant. Convert quantities to scientific significant. Convert quantities to scientific notation to remove the placeholder zeros.notation to remove the placeholder zeros.

5.5. Counting numbers and defined constants have Counting numbers and defined constants have an infinite number of significant figures.an infinite number of significant figures.

RoundingRounding

When do you round and how?When do you round and how?

RoundingRounding

A calculated value with eight significant A calculated value with eight significant figures is not appropriate when you only need figures is not appropriate when you only need four significant figures.four significant figures.

Rules for RoundingRules for Rounding1.1. If the digit to the immediate right the last significant If the digit to the immediate right the last significant

figure is less than five, do not change the last figure is less than five, do not change the last significant figure.significant figure.

2.2. If the digit to the immediate right of the last significant If the digit to the immediate right of the last significant figure is greater than five, round up the last significant figure is greater than five, round up the last significant figure.figure.

3.3. If the digit to the immediate right of the last significant If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero figure is equal to five and is followed by a nonzero digit, round up the last significant figure.digit, round up the last significant figure.

4.4. If the digit to the immediate right of the last significant If the digit to the immediate right of the last significant figure is equal to five and is not followed by a nonzero figure is equal to five and is not followed by a nonzero digit, look at the last significant figure. If it is an odd digit, look at the last significant figure. If it is an odd digit, round it up. If it is an even digit, do not round digit, round it up. If it is an even digit, do not round up.up.

Organizing DataOrganizing Data Scientists accumulate vast amounts of Scientists accumulate vast amounts of

data by observing events and making data by observing events and making measurements. measurements.

Interpreting these data can be a Interpreting these data can be a difficult task if they are not organized. difficult task if they are not organized.    

Scientists can organize their data by Scientists can organize their data by using data tables and graphsusing data tables and graphs. .

These tools make it easier to spot These tools make it easier to spot patterns or trends in the data that can patterns or trends in the data that can support or disprove a hypothesis support or disprove a hypothesis

Data TablesData Tables The simplest way to organize The simplest way to organize

data is to present them in a data is to present them in a table. table.

The table relates two variablesThe table relates two variables—an independent variable —an independent variable and a dependent variable. and a dependent variable.

xx yy

11 22

33 44

55 66

Line GraphsLine Graphs

A line graph is useful for showing changes that occur A line graph is useful for showing changes that occur in related variables. in related variables.

In a line graph, the independent variable is generally In a line graph, the independent variable is generally plotted on the horizontal axis, or plotted on the horizontal axis, or xx-axis. -axis.

The dependent variable is plotted on the vertical axis, The dependent variable is plotted on the vertical axis, or or yy-axis, of the graph. -axis, of the graph.

A A direct proportiondirect proportion is a relationship in which the is a relationship in which the ratio of two variables is constant. ratio of two variables is constant.

An An inverse proportioninverse proportion, a relationship in which the , a relationship in which the product of two variables is a constant. product of two variables is a constant.

Bar GraphsBar Graphs

A bar graph is often used to compare a set of A bar graph is often used to compare a set of measurements, amounts, or changes. measurements, amounts, or changes.

The bar graph makes it easy to see how the The bar graph makes it easy to see how the data for one thing compares with the data for data for one thing compares with the data for another.another.

Circle GraphsCircle Graphs

A circle graph is a divided circle A circle graph is a divided circle that shows how a part or share of that shows how a part or share of something relates to the whole. something relates to the whole.

Communicating DataCommunicating Data

A crucial part of any scientific investigation is reporting A crucial part of any scientific investigation is reporting the results.   the results.  

Scientists can communicate results by writing in scientific Scientists can communicate results by writing in scientific journals or speaking at conferences. journals or speaking at conferences.

Scientists also exchange information through Scientists also exchange information through conversations, e-mails, and Web sites. conversations, e-mails, and Web sites.

Young scientists often present their research at science Young scientists often present their research at science fairs fairs

Peer ReviewPeer Review

Different scientists may interpret the same data Different scientists may interpret the same data differently. This important notion is the basis for differently. This important notion is the basis for peer peer reviewreview, a process in which scientists examine other , a process in which scientists examine other scientists' work. scientists' work.

Peer review encourages comments, suggestions, Peer review encourages comments, suggestions, questions, and criticism from other scientists.questions, and criticism from other scientists.

Peer review can also help determine if data were Peer review can also help determine if data were reported accurately and honestly. reported accurately and honestly.