Metric Units and Measurement

Units of MeasurementWhy do we need a “standard” unit of Measurement?– Report Data that can be reproduced

Base Units– Time = Seconds (s)– Length = meter (m)– Mass = kilogram (kg) – Volume = space occupied by an object• Liter (L)

Metric Units

Derived Units Continued

or

Now What are the units for the following?– Mass = ?• Grams or g

– Volume = ?• mL or cm3

Now… Insert them into the formula!

Derived Units

Now What are the units for the following?– Mass = ?• Grams or g

– Volume = ?• mL or cm3

= Combination of base unitsExample: Density• Density = Mass Divided by Volume– How would we write this? Use symbols.

Density

So… Density is the Ratio of Mass to Volume.

Determining Volume• Here is an odd shaped Object…

• How would you find the volume if you couldn’t take any measurements?

• Water displacement that’s how…• What happens when you get into a bath tub

that is filled to the top with water?– That’s right it over flows! Why..

Water displacement

Water Displacement• Let’s take our object• And a graduated Cylinder filled with some water… enough to cover the object• … but not completely filled (remember what

happened to the bath tub!)

Water Displacement and Volume• What would happen if we placed our object… into the graduated cylinder?

• The Water level starts at..– 46 mL

• Ends at 66 mL• What’s the difference…– 20 mL– That’s the volume of the object

Using the Density formula answer the following questions.

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

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

Units• All measurements start with the base unit– Length is m or meters– Volume is L or liters– Mass is g or grams

• How ever… what if the object is less than the base unit?

• Let’s look at length or meters (m)1 meter

Units continues

• Each unit (m, L, g) is broken down into parts of 10• Lets break this meter stick into 10 parts

1 meter

1 2 3 4 5 6 7 8 9 10

• Each part is 1/10th of a meter• Each part is called a decimeter or dm• So… what is the length of this nail?– 4 dm or 4 decimeters

• This is 1 dm

• This is 1 cm• This is 1 mm

Prefixes Used with SI Units

Examples

Centimeter = ?– 100th of a meter or .01 or 10-2

Kilometer = ?– 1000 meters or 10 3

Millimeter– 1000th of a meter / or .001 / or 10-3

TemperatureWhat is the SI Unit of Temperature?– Kelvin (K)• 273 K = freezing point of water• 373 K = boiling point of water

What’s the difference between the two?– 100 degrees

What is Celsius?– Temperature measurement based on 0o – 100o C

We will always convert Celsius to Kelvin, unless told not to.

Converting Kelvin to CelsiusConvert - Celsius to Kelvin– oC (what you measured) + 273 K = Kelvin

Convert – Kelvin to Celsius– oK (what you measured) – 273 K = oCelsius

Convert the following to Kelvin– 357o C– -39o C

Convert the following to Celsius– 266 K– 332 K

Activity – miniLAB - Density• Follow the directions on page 15 of your book• We will be doing a lab write up on this lab.

NEXT CLASS: Chapter 2:1 / 2:2

•Homework: WB 2:1 / 2:2•Quiz 3: Day 5 (Chapter 2:1 / 2:2)

TODAY: Chapter 2:2 / 2:3DAY 5– NO QUIZ!!! – Density LAB– Sections 2 AND 3– Next Class Sections 2 AND 3– HW: Sections 2 and 3

Homework:– Homework: WB 2:2 / 2:3

• Quiz 3: Day 6 (Chapter 2:2 / 2:3)

Density Lab• Materials;– Cork stopper, Rubber stopper, Nut and bolt– Graduated cylinder, water

Formula:D=M/V

Data Table:MASS VOLUME DENSITY

Final (mL) Initial (mL) Volume

Cork StopperRubber Stopper

Nut & Bolt

Convert to Scientific NotationPretest• 134,000• 5,400• 0.001034• 0.00078

Scientific NotationWhat's the goal of Scientific Notation?– Condense the number that is written

Example: What would you rather write– 0.00000000000000000456

Or– 4.56 x 10-18

Rules of Scientific Notation• It’s all about the decimal point! And power of 10!Example: 645,0001st… move the decimal point so one # is to the left

of it6.45000

2nd… place “x 10” to the right6.45000 x 10

3rd… count the number of spaces you moved the decimal point.

6.45000 X 105

Almost Done!

• 6.45000 X 105

Now get rid of the zeros6.45 X 105

Rules: #1..moving the decimal point to the left…

the exponent gets bigger #2… moving the decimal point to the right…

the exponent gets smaller 64.5 X 10… what's the exponent

6.45 X 104

Adding ExponentsRules:1st… exponents need to be the same. Move the decimal point until the two numbers have the same exponent2nd… add OR subtract the numbers… not the exponents.Example: Add the following #s…Follow the Rules

6.45 x 105

3.11 x 104

Answer: 6.76 x 105

Practice problems pg 32Addition and Subtraction•Every problem

Pretest

• Multiply (2 x 103) x (3 x 102)

• Divide (9 x 108) ÷ (3 x 10-4)

Multiplying / Dividing

MultiplyingRules:– 1st… multiply the numbers– 2nd… add the exponents

DividingRules– 1st… divide the numbers– 2nd… subtract the exponents

Practice Problems pg 33Multiply(2 x 103) x (3 x 102) =

Divide(9 x 108) ÷ (3 x 10-4) =

ConversionsRules:1st… write down what you know2nd… write down what you want to know3rd… what conversion factor are you going to use to

get there?Convert 48km to meters (factor: 1km=1000meters)

=______m1000𝑚1𝑘𝑚

48𝑘𝑚1

1𝑘𝑚1000𝑚

1000𝑚1𝑘𝑚

or

48000

Types of Measurements• Precise vs. Accurate

Percent Error• The Accepted value is a known value• Error = Accepted - Measured

% error example• The accepted density for copper is 8.96g/mL.

Calculate the percent error for each of these measurements.

• 8.86 g/mL• 8.92 g/mL• 9.00 g/mL• 8.98 g/mL

1.11%.45%.45%

.22%

Significant Figures or Sig FigsTells the how precise the measurement is• Example: Which is more precise?

3.5 or 3.52g

Rules for Sig Figs – pg. 391. Non-zero umbers are always significant2. Zeros between non-zero numbers are always

significant3. All final zeros to the right of the decimal place are

significant.4. Zeros that act as placeholders are NOT significant.

Convert quantities to scientific notation to remove the placeholders.

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

Examples – use your rules• Which numbers are significant?

72.360.56.200.02534320125000

• Help yourself out – convert to Scientific Notation

Rounding Numbers – pg 401. If the digit to the immediate right of the last sig fig is

less than five, do not change the last sig fig.2. If the digit to the immediate right of the last sig fig is

greater than five, round up the last sig fig3. If the digit to the immediate right of the last sig fig is

equal to five and is followed by a nonzero digit, round up the last sig fig.

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