Physical Science 1-5: Measurement & Math

Physical Science 1-5: Measurement & math in Physical Science

Multiple Choice

What is a model?

• A sequence of actions in a system

• A representation of a complex object or process

• A group of parts that work together

• Material that goes into a system

Multiple Choice

What is this?

• Balance
• Test Tube

• Beaker

• Graduated cylinder

Multiple Choice

What is this piece of equipment?

• erlenmeyer flask

• florence flask

• beaker

• test tube

Multiple Choice

What is the piece of equipment shown in the picture?

• scoopula

• pipette

• crucible tongs

• beaker tongs

Multiple Choice

The Curved surface of the liquid in a graduated cylinder - always read the bottom!

• graduated cylinder

• meter stick

• meniscus

• volume

Lesson Objectives

• Describe the system of measurements used in science

• Perform basic data calculations

  • Unit conversions

  • Averages

  • Percent Error

How do scientists Record Measurements?

• In everyday life, different countries use different units of measurement

  • Units can depend on certain situations

• Since scientists communicate with people all over the world, they have agreed to use the same units of measurement to keep things consistent

• The Metric system used in science

  • Written in multiples of 10 for easy conversion

• ​There are seven base units in SI Measurement

  • In Physical science, we will focus on some units more than other

    • mass

    • volume

    • length/distance

    • temperature

​The International System of Units

Length

• The Base SI unit is a Meter

  • In class, we will mostly use centimeters

• Tells the distance or height/length of an object

• Measured using:

  • a meter stick

  • a ruler

  • a tape measure

    • Make sure you are using the correct side

Mass

• Base Unit is the Kilogram (Kg)

  • When we use smaller objects in the class, we will measure them in grams

• Mass tells you the amount of matter in an object

  • NOT how much something weighs

• Measured on the electric balance or the Toledo Scale on the back for larger objects

Volume

• Volume: The amount of space that something fills

• The unit depends on what the substance being measured is made of

  • Liquids: Liters

  • Solids: Cubic Meters

• Solids Can be measured in different ways that we will explore throughout the year

• Liquids are measured in a graduated cylinder

Tempurature

• Temperature: A measurement of the average kinetic energy of particles in an object

  • Energy creates heat, which is what we feel when we say an object is "hot"

• The SI unit for Temperature is Kelvin, but we will mainly use Celsius

  • An easier scale for comparison

• Measured using thermometers and temperature probes

Multiple Choice

What is mass a measure of?

• The force of gravity on an object

• The amount of matter in an object

• The volume of an object

• The density of an object

Multiple Choice

Which of the following is a METRIC unit of measure for LENGTH?

• mL

• in.

• kg

• cm

Multiple Choice

Which unit is used to measure Mass of an object?

• Centimeters
• Milliliters
• Grams
• Volume

Multiple Choice

What would you use a RULER for?

• To measure length.

• To measure mass.

• To measure volume.

• To measure time.

Multiple Choice

Which of the following is a METRIC unit of measure for VOLUME?

• mL

• cups

• kg

• cm

Converting between Units

• When using the SI system, you scale the base unit up or down using different prefixes

  • Prefixes are the same for all units, but some are used more often with specific units

• We can convert between units using the Unit Factor Method

  • Uses the ratio as a fraction between two values to scale the units

    • Follows the rules of cross-canceling from math

Converting between Units Sample Problem 1

• A ball is dropped from a height of 25 cm. What is the same distance described in meters?

  • Step 1: Identify the two units you are converting between

    • Centimeters and Meters

  • Step 2: Establish the relationship between the two units

    • 1 meter = 100 cm

  • Step 3: Set up your ratio as a conversion factor

    • The unit you start with should be able to cross-cancel

Converting between Units Sample Problem 1

• A ball is dropped from a height of 25 cm. What is the same distance described in meters?

  • Step 1: Identify the two units you are converting between

    • Centimeters and Meters

  • Step 2: Establish the relationship between the two units

    • 1 meter = 100 cm

  • Step 3: Set up your ratio as a conversion factor

  • Step 4: Plug into your calculator and solve

Fill in the Blanks

A ball is dropped from a height of 25 cm. What is the same distance described in meters?

Converting between Units Sample Problem 2

• A small cube has a mass of 5.712 grams. Express this mass in milligrams

  • Step 1: Identify the two units you are converting between

    • Grams and Milligrams

  • Step 2: Establish the relationship between the two units

    • 1 gram = 1000 mg

  • Step 3: Set up your ratio as a conversion factor

Converting between Units Sample Problem 2

• A small cube has a mass of 5.712 grams. Express this mass in milligrams

  • Step 1: Identify the two units you are converting between

    • Grams and Milligrams

  • Step 2: Establish the relationship between the two units

    • 1 gram = 1000 mg

  • Step 3: Set up your ratio as a conversion factor

Fill in the Blanks

A small cube has a mass of 5.712 grams. Express this mass in milligrams

Converting between Units Sample Problem 3

• A car travels a distance of 16.45 meters. How far is this in Kilometers?

  • Step 1: Identify the two units you are converting between

    • Meters and Kilometers

  • Step 2: Establish the relationship between the two units

Multiple Choice

What is the relationship between meters and kilometers?

• 1 kilometer = 500 meters
• 1 kilometer = 1,000 meters
• 1000 kilometer = 1 meter

• 1 kilometer = 100 meters
• 100 kilometers=1 meter

Converting between Units Sample Problem 3

• A car travels a distance of 16.45 meters. How far is this in Kilometers>

  • Step 1: Identify the two units you are converting between

    • Meters and Kilometers

  • Step 2: Establish the relationship between the two units

    • 1 kilometer = 1000 meters

  • Step 3: Set up your ratio as a conversion factor

  • Step 4: Plug into your calculator and solve

Converting between Units Sample Problem 3

• A car travels a distance of 16.45 meters. How far is this in Kilometers?

  • Step 1: Identify the two units you are converting between

    • Meters and Kilometers

  • Step 2: Establish the relationship between the two units

    • 1 kilometer = 1000 meters

  • Step 3: Set up your ratio as a conversion factor

  • Step 4: Plug into your calculator and solve

Fill in the Blanks

A car travels a distance of 16.45 meters. How far is this in Kilometers?

Fill in the Blanks

Express of a mass of 0.014 mg in grams.

Fill in the Blanks

1.57 kilometers is how many meters?

Averages

• When we do different measurements, we can sometimes get different results each time

  • Which number is the most correct?

• To get the best representation of data, we take the average of a dataset

• To calculate your average

  • Add all of your data points/trials together

  • Divide by how many data points/trials you have

Averages Sample Problem 1

• In a garden, there are four trees. The trees measure 4 meters, 7 meters, 2 meters, and 3 meters. What is the average height of the trees?

  • Step 1: Add together all the data points you have

    • 4+7+2+3=16

  • Step 2: Divide the sum of all measurements by the total number of data points

Fill in the Blanks

In a garden, there are four trees. The trees measure 4 meters, 7 meters, 2 meters, and 3 meters. What is the average height of the trees?

Averages Sample Problem 2

• A group of customer service surveys were sent out at random. The scores were 90, 50, 70, 80, 70, 60, 20, 30, 80, 90, and 20. What was the average score?

  • Step 1: Add together all the data points you have

Fill in the Blanks

A group of customer service surveys were sent out at random. The scores were 90, 50, 70, 80, 70, 60, 20, 30, 80, 90, and 20. What is the sum of all the scores?

Averages Sample Problem 2

• A group of customer service surveys were sent out at random. The scores were 90, 50, 70, 80, 70, 60, 20, 30, 80, 90, and 20. What was the average score?

  • Step 1: Add together all the data points you have

    • 660

  • Step 2: Divide by the total number of data points there are

    • There are 11 data points

Fill in the Blanks

A group of customer service surveys were sent out at random. The scores were 90, 50, 70, 80, 70, 60, 20, 30, 80, 90, and 20. What is the average of the scores?

Averages Sample Problem 3

• A lab group is trying to see how many drops of water they can fit on a penny. Find the average number of water drops from their data: 22 drops, 40 drops, 37 drops

  • Step 1: Add together all the data points you have

Fill in the Blanks

Add the following data points together: 22 drops, 40 drops, 37 drops

Averages Sample Problem 3

• A lab group is trying to see how many drops of water they can fit on a penny. Find the average number of water drops from their data: 22 drops, 40 drops, 37 drops

  • Step 1: Add together all the data points you have

    • 99

  • Step 2: Divide by the number of trials they did

Fill in the Blanks

Find the average number of water drops:

22 drops, 40 drops, 37 drops

Fill in the Blanks

Find the average of these numbers: 10, 4, 5, 9

Fill in the Blanks

Calculate the average time for 10 g of granulated sugar to dissolve. Round to 2 Decimal Places!

Fill in the Blanks

Calculate the average of the set of data: 4.23, 7.40, 1.03, 8.26, 5.34, 3.88

Percent Error

• Some information in science we know through repeated trials

  • Example: Water boils at 100 degrees Celsius and freezes at 0 degrees Celsius

• The accuracy of a given value can be compared to the result you get in an experiment

  • can be useful for evaluating your lab methods and equipment

• Can be positive if the experimental value is bigger, or negative if the experimental value is smaller

Percent Error Sample Problem 1

• What is the percentage error for a mass measurement of 17.7 g

  given that the correct value is 21.2 g?

  • Step 1: Identify the variables in the Percent Error Equation

    • Experimental=17.7

    • Actual=21.2

  • Step 2: Plug the values into the percent error equation and solve

Fill in the Blanks

What is the percentage error for a mass measurement of 17.7 g, given that the correct value is 21.2 g? Round to a whole Number!!

Percent Error Sample Problem 2

• A student measures the mass of a sample as 9.67 g. Calculate the percentage error, given that the correct mass is 9.82 g.

  • Step 1: Identify the values in the equation

Match

Match the following information to what it represents in the problem

• Percent Error

• 9.67 g

• 9.82 g

Unknown

Experimental Value

Actual Value

• Unknown

• Experimental Value

• Actual Value

Percent Error Sample Problem 2

• A student measures the mass of a sample as 9.67 g. Calculate the percentage error, given that the correct mass is 9.82 g.

  • Step 1: Identify the values in the equation

    • Experimental = 9.67

    • Actual=9.82

  • Step 2: Plug values into the percent error equation and solve

Fill in the Blanks

A student measures the mass of a sample as 9.67 g. Calculate the percentage error, given that the correct mass is 9.82 g. Round to One Decimal Place!!

Percent Error Sample Problem 3

• What is the percentage error of a length measurement of 0.229 cm if the correct value is 0.225 cm?

  • Step 1: Identify the values in the equation

Multiple Choice

What is the percentage error of a length measurement of 0.229 cm if the correct value is 0.225 cm?

Which value is the experimental?

• 0.229

• 0.225

• 0.004

• 100

Multiple Choice

What is the percentage error of a length measurement of 0.229 cm if the correct value is 0.225 cm?

Which value is the actual?

• 0.229

• 0.225

• 0.004

• 100

Percent Error Sample Problem 3

• What is the percentage error of a length measurement of 0.229 cm if the correct value is 0.225 cm?

  • Step 1: Identify the values in the equation

    • Experimental = 0.229

    • Actual = 0.225

  • Step 2: Plug into our equation and solve

Fill in the Blanks

What is the percentage error of a length measurement of 0.229 cm if the correct value is 0.225 cm? Round to a Whole Number!!

Fill in the Blanks

Bob estimates that there will be 230 people who attend the concert.  A total of 300 people actually attended.  Find the approximate percent error.  Round to a Whole Number.