Measurement

Mr. Martin

1. Distance (Length)

How wide is the floppy disk?

How wide is the black metal tab?

Measure Accurately

Measuring Length of Book

Zero mark at one edge of book. Read measurement at other edge.

Here you can read to the nearest tenth of a cm.

Breaking News!•King Hector died Monday drinking chocolate milk!

King Hector died Monday drinking chocolate milk.Kilo hecto deca meter deci centi milli

• Kilometer (km) 1000m• Hectometer (hm) 100m• Decameter (dam) 10m• Meter (m) 1m• Decimeter (dm) .1m• Centimeter (cm) .01m• Millimeter (mm) .001m• Micrometer (um) .000001m• Nanometer (nm) .000000001m

You try and measure some distances.

• Width of table in cm? in meters? in decimeters?• Length of table in cm? in meters? in decimeters?• Width of Pre-Algebra math book in cm? in meters?• Length of Pre-Algebra math book in cm? in meters?• Depth of Pre-Algebra math book in cm? in mm?• Dimensions (length and width) of floor of room in

meters? • Length of pencil? (You choose appropriate metric

measure)• Diameter of a coin? (You choose the coin and the

appropriate metric measure)

Conversions(Why King Hector is important!)

• King Hector died Monday drinking chocolate milk!• K H D M D C M

You Try!

• 5.75m = _____ cm

• 5.8km = _____ m

• 1,345cm = _____m = _____ dam = ____dm

• 52cm = _____m = ______km

• 127mm = _____ cm = _____m = ______dm

• 0.056km = _____m = _____cm

2. Area• Definition – Number of square units that fit

into a two dimensional space.

7cm

5cmArea = 5cm x 7cm= 35 cm2 = 35 squarecentimeters

Area Applications• The square feet in a house.

– In metric, the square meters in a house.

• The square feet of carpet in the classroom.– In metric, the square meters of carpet in the

classroom.– Calculate it!

• The area in square centimeters of the cover of the Pre-Algebra book.– Calculate it!

Big Areas• Large areas of land in the United States are

frequently measured in acres.– One square mile, which is called a section, has 640

acres. Therefore, one acre is 1/640 of a square mile.

– One mile = 5280 feet. One square mile is hence equal to 5280 feet x 5280 feet = 27878400 square feet. One acre is 1/640 times 27878400 = 43,560 square feet.

• Large areas of land in the metric system are measured in Hectares.

• 1 hectare is equal to 10,000 square meters (100 meters x 100 meters)

• 1 hectare is about 2.5 acres

3. Volume

• Definition volume – the amount of three dimensional space an object occupies.– Measured in cubic units such as cubic meters,

cubic centimeters, etc.

1cm

1cm

One Cubic Centimeter

(cm3)

1m

1m

1m

One Cubic

Meter

1cm1cm

What’s the volume?Calculate it!

• Answer?– 140 cm3

• Answer?– 280m3

7cm

4cm

5cm

7m

10m

4m

The cube is one decimeter by one decimeter by one decimeter

• What is the volume in cubic decimeters?1 dm3

• What is the volume in cubic centimeters?

• Clue: What are the dimensions in cm?10cm x 10cm x 10cm =

1,000 cm3

Some Interesting Volume Names• 1 cubic decimeter = 1,000 cubic centimeters =

1 Liter (L)• 1 cubic centimeter (cm3) is abbreviated in

medicine frequently as cc. • 1 cm3 = 1 cc = 1 milliliter = 1 mL• 1 mL of water at standard temperature and

pressure has a Mass of 1 gram (gm)• 1 L of water at standard temperature and

pressure has a Mass of 1 kilogram (Kg)– More on Mass later

Practice with Metric Volume

• Find the volume of the classroom in:– Cubic meters– Liters (Remember a liter is a cubic decimeter)– Milliliters (Remember a mL is a cubic cm)

King Hector died Monday drinking chocolate milk! (Again!)

• King Hector is useful for converting metric units of volume also

• King Hector died Monday drinking chocolate milk!• K H D M D C M

You Try!

• 57.5L = _____ dL (deciliter)=_____mL

• 5.2mL = ____ cc = ____ cm3

• 5.8m3 = _____ L

• 1,345mL = _____L = _____ dL

• 52kL = _____L

• .05L = ____ mL

• 1mL = ____L

Homework1. Use a tape measure to measure the

dimensions of your bedroom. Use 2.5m for the height of the room. (I don’t want you climbing!) Ans. ______________

2. What is the area of the floor in square meters? ________________________

3. What is the area of any one of your walls in square meters? _________________

4. What is the volume of your room in cubic meters? ___________ In liters? _______

Date: _________________ Name: ________________

Common Places Where Volume is Used

• Diet Coke can holds 355 mL of Diet Coke

• Water bottle holds 500 mL or 0.5 L of water

In chemistry, we can measure volume with a flask, beaker or more accurately

with a graduated cylinder

Graduatedcylinder beaker

Erlenmeyer flask

Volume from Geometry

• Coke can has inner diameter of about 6.1cm and a height of about 12 cm

• It is roughly a cylinder• Area = area base x

height = Πr2h = 3.14x3.05cmx3.05cmx12cm= 351 cm3, which is close to what the Coke can says

Volume from Graduated Cylinder

• Or pour the liquid into a graduated cylinder

How do I find the volume of the rock?

Ideas?• Does this give

you an idea?

• It reads 200 mL at the bottom of the meniscus.

• How does this help in finding the volume of the rock?

What do I do with the rock?• Put rock in water• See how much water it

displaces• That equals the volume of the

rock• Here, the original volume of the

water was 200mL• The new volume is about

245mL• The volume of the rock is

245mL – 200mL = 45mL

4. Mass• Mass- the measure of the amount of matter in an

object• Root prefix unit is gram (In SI the base unit is kilogram.

A gram is 1/1000 of a kilogram.)• King Hector died Monday drinking chocolate milk• kilo hecto deca (gram) deci centi milli• As a practical matter, people primarily use kilogram

(1,000 grams), grams and milligrams (.001 gram or 1/1,000 of a gram)

• Informally, a kilogram is about 2.2 pounds, a paper clip has a mass of about 1 gram and a new penny has a mass of about 2.5 gram. Milligrams are very small and are frequently used to measure the mass of medicines.

Mass versus Weight• In everyday language, people often use mass and

weight interchangeably. They are different, however.• Weight is the mass of an object multiplied by its

acceleration due to gravity. Weight is a force. In the metric system it is measured in Newtons. In customary units it is measured in pounds.

• Your mass is same on earth as it is on the moon.• Your weight on earth is different from your weight on

the moon since there is less gravity on the moon. If I weigh 100 pounds on earth, I would weigh only 16.6 pounds on the moon. I would weigh 236.4 pounds on Jupiter. (http://www.exploratorium.edu/ronh/weight/)

How to Measure Mass• Mass is measured with a balance like the

simple balance or triple beam balance below

Simple Balance

Triple Beam Balance

Measuring Mass with Triple Beam Balance• Set object on pan• Move largest mass (middle) to point just before

balance tips• Move mass in back to point just before balance tips• Move smallest mass (front) until line is exactly at zero

A Scale Measure Weight, Not Mass• The spring scale here technically

measures weight, not mass• Weight is a force that is equal to the

mass times the acceleration of gravity• This scale will show different weights

on earth and the moon. A balance will give the same measure of mass.

• The metric unit for weight is a Newton• This spring scale actually reads in

grams, however, a unit of mass. It is a reasonably accurate measure of mass on earth.

A Digital Scale• While technically a

scale that measures weight, this is set up to measure mass in grams also

• It would not give an accurate mass on the moon

• Here, the rock has a mass of 115 grams

• It is precise to the nearest gram

A digital scale is fast and easyto use.

5. Density

• Density is mass divided by volume

• I.e., density is mass per unit volume

• A measure of density is grams/mL

Each is about the same volume.

Which one has the greater density?

Table Tennis Ball

Golf Ball

Let’s find the density of each.

Table Tennis Ball• Diameter of table tennis

ball is: __________ • Find volume: ________• Mass of table tennis ball

is: ______________(Use balance to measure)

• Density = Mass/Volume• Make sure you have

appropriate units in the result

Volume of sphere = 34

3r

Golf Ball• Diameter of golf ball is:

__________ • Find volume: ________• Mass of golf ball is:

______________

(Use balance to measure)• Density = Mass/Volume• Make sure you have

appropriate units in the result

Measuring the Mass with Triple Beam Balance

Let’s see the resultTable Tennis Ball• Diameter of table tennis

ball is: 3.6 cm• Find volume:

• Mass of table tennis ball is: 2.6g

• Density = Mass/Volume

2.6g/24.43mL = 0.106g/mL

Golf Ball• Diameter of golf ball is:

4.0 cm• Find volume:

• Mass of golf ball is: 46.0g

• Density = Mass/Volume

46.0g/33.51mL =

1.37 g/mL

3 34(3.14)(1.8 ) 24.433

cm cm 3 34(3.14)(2.0 ) 33.513

cm cm

The golf ball is almost 13 times more dense. (1.37/.106 =12.9)

You Do It!Determine the density of the tennis

ball and baseball.

Find the density of each.

Tennis Ball• Diameter of tennis ball is:

__________ • Find volume: ________• Mass of tennis ball is:

______________(Use balance to measure)

• Density = Mass/Volume• Make sure you have

appropriate units in the result

Volume of sphere = 34

3r

Baseball• Diameter of baseball is:

__________ • Find volume: ________• Mass of baseball is:

______________

(Use balance to measure)• Density = Mass/Volume• Make sure you have

appropriate units in the result

• How hot or cold a substance is

• A measure of the average kinetic energy of an object

• Two common scales to measure – Celsius and Fahrenheit

• Celsius is used in science and in countries using the metric system

6. Temperature

0ºC

100ºC

32ºF

212ºF

WaterFreezes

WaterBoils

Celsius Fahrenheit

Converting from Fahrenheit to Celsius and Celsius to Fahrenheit

932

5F C

If you know the Celsiustemperature, you can convertto Fahrenheit by plugging inthe Celsius temperature in thisformula.

1.8 32F C The same formula in decimalform.

5( 32)9

C F If you know the Fahrenheittemperature, you can convertto Celsius by plugging inthe Fahrenheit temperaturein this formula.It’s good to know at least the top formula since they show up on standardized tests.If you know the top formula, you can also solve for C to get the bottom formula.

If you are familiar with the slope intercept form of a line, you can figure out the formulas. 9

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