Measurement

Vocabulary

Metric System Meniscus

Mass Density

Weight VolumeVolume Displacement

SI (International System of Units)

Measurement Systems

Measurement is fundamental to our society

Over 200 years ago, there were many different measurement systems

One of the first tools developed by humans was measurement

1

Measurement Systems“Weights and measures may be ranked among the necessaries

of life to every individual of human society. They enter into the economical arrangements and daily concerns of every family. They are necessary to every occupation of human industry; to the distribution and security of every species of property; to

every transaction of trade and commerce; to the labors of the husbandman; to the ingenuity of the artificer; to the studies of

the philosopher; to the researches of the antiquarian; to the navigation of the mariner, and the marches of the soldier; to all the exchanges of peace, and all the operations of war. The knowledge of them, as in established use, is among the first

elements of education, and is often learned by those who learn nothing else, not even to read and write.”

JOHN QUINCY ADAMS - Report to the Congress, 1821

What if measurement tools and equipment did not exist?

Metric Units

Kilo/ Hecto/ Deka/ (Base) Unit/ Deci/ Centi/ Milli

King Henry Doesn't Usually Drink Chocolate Milk

Why is it important to have a standard system?

International System of Units (SI) A version of the metric system used by scientists

all over the world.

Systeme International d’Unites

Standard system of measurement that allows scientists to compare data and communicate with each other about their results.

Based on powers of 10Powers of 10 video

SI UnitsUnits:

Length: Meter (m)

Mass: Kilogram (kg)

Time: Second (s)

Temperature: Kelvin (K)

Amount of Substance: Mole (mol)

Electric Current: Ampere (A)

Luminous Intensity: Candela (cd)

Derived Units:Volume: cubic meter (m3)

Density: grams per cubic centimeter (g/cm3)

Others:SpeedForcePressureEnergy

Common Measurement ToolsLength Mass and Weight Volume

Length, Time and TemperatureTime

SI unit = Second (s)

Tools used to measure time: stopwatch, clock, etc.

Length

SI unit = Meter (m)

Tools used to measure length: Meter stick, measuring tape, etc.

Temperature

SI unit = Kelvin (k)

Tools used to measure temperature: thermometer.

TemperatureA measure of the average energy of motion of the particles of a substance.

3 scales used to measure temperature: Fahrenheit, Celsius, and Kelvin

On the Celsius scale, 0 = Freezing and 100 = Boiling

0 Kelvin = Absolute Zero, the temperature at which no more heat can be removed- there is not a temperature that is colder. Kelvin is the SI unit, and it is often used in science because it does not have negative numbers.

Temperature

Fahrenheit Celsius Kelvin

Absolute Zero

-459 -273 0

Freezing 32 0 273

Boiling 212 100 373

What has more mass- a pound of feathers or a

pound of rocks?

Which is more dense?

Mass v. WeightMass and Weight are not the same

Mass (the resistance to change in motion)-inertia A measure of amount of matter an object contains. Does not change when the object’s location is changed. Measured using a triple-beam balance SI unit is Kilogram (kg).

Weight (a force) A measure of the force of gravity acting on an object. Weight = mass x gravity Weight does change depending on where an object is located. SI unit is the Newton (N).

Example: If you go to the moon with a rock with a mass of 200 grams (on Earth), it will still have a mass of 200 grams on the moon. However, the rock will feel lighter because the force of gravity is not as strong. It’s weight will be less.

Volume Volume: is a measure of the amount of space an object occupies. The SI unit for volume is the cubic meter (m3)Measuring Volume: use a graduated cylinder or a metric ruler

Liquids: Use a container with volume markings. Units are in Liters (l) or Milliliters (ml).

Solids: Volume= Length x Width x Height

Volume = 5 cm x 6 cm x 10 cm = 300 cm3

Irregular solids: Place the object in water and measure how much the water rises (displacement of water).

Density

Density: is a measure of how much mass is contained in a certain volume.

Density= mass/volume It is a derived SI measurement from the

measurements of mass and volume. Density is a physical characteristic of a substance. Example: If you have a small glass of water and

compare the water’s density to that of a huge lake, you find that the density is the same.

The units of measurement are g/cm3

Math Skills Important for Science

Estimation Accuracy and Precision Significant Figures and Scientific Notation Unit Conversion Mean, Median, Mode, Range Percent Error Graphing and analyzing data

Estimation An estimate is an approximation of a number based on

reasonable assumptions.

It is not guessing.

It is based on known information.

Estimates are used by scientists when they cannot use exact numbers.

Examples: Astronomers cannot measure the distance between the

stars. They use indirect measurements and models

Park rangers cannot count all the trees in a forest.

How could we estimate the number of students in the school if we did not know?

Accuracy and Precision Accuracy: How close a measurement is to the true or

accepted value.

Precision: How close a group of measurements are to each other.

Both accuracy and precision are important in measurements.

The more precise and accurate the measurements, the more reliable the data

Why do measurements need to be precise and accurate?

Accuracy v. Precision

http://www.batesville.k12.in.us/physics/apphynet/Measurement/Accuracy_Precision.html

Accuracy and Precision

How to achieve accuracy and precision:

1. Use high quality measurement tools

2. Make measurements carefully

3. Repeat the measurement several times

What about measurements-Why would there be uncertainty in our measurements?

Can numbers be exact?

Significant Figures All the digits in a measurement that have been measured exactly,

plus one digit whose value has been estimated are significant figures.

Values that are important in a measurement- they tell you how certain you are about a measurement.

The number of sig figs you write for a measurement tell you how precise your measurement is based on the equipment you are using.

The last digit tells others that you are not certain about that number-it is estimated.

Significant Figures Measurements always have some level of uncertainty

Measurements are uncertain due to:

Limitations in our measurement tools Human error Limitations in our ability to see and interpret measurements Manufacturing process limitations

Every tool that you use will have a different number of significant figures because there is a different level of certainty

Measuring with Proper Sig Fig’s

How would measurements using these two different graduated cylinders be different?

10 ml 10.0 ml

Measuring with Significant Figures

Measurements should only contain significant figures Example: the measurement 5.36 cm has 3 significant

figures; the 6 has been estimated. In most cases zero’s are counted as significant figures. Examples:

the measurement 10.5 g has ______________ significant figures.

The measurement 100,045.360 m has ____________ significant figures.

What would my data be reporting if I said my measurement was 10.453 g instead of

10.5g?

Why do we need to account for this uncertainty in

measurements?

Scientific Notation

http://www.lasalle.edu/~smithsc/Astronomy/Units/sci_notation.html

-Helps reduce ambiguity in the significance of zeros in a measurement-Helps make it easier to work with really BIG or really small numbers

Converting to Scientific Notation

Basic rule: The exponent in scientific notation is equal to the number of times you move the decimal to the left or right to produce a number between 1 and 10.

If you move it right – it is a negative exponent EX. 0.06078 = 6.078 x 10-2

If you move it left- it is a positive exponent EX. 10,567 = 1.0567 x 104

Converting to Scientific Notation

Write the following in scientific notation:

0.32

345

.00000045

32000000

32000000.

5.31

Unit Conversion (Dimensional Analysis

To convert between units you must use a conversion factor.

The conversion factor is a fraction:

The numerator: the units that you want in your answer The denominator: the units that you start with

Example 1: Convert 12 inches to centimeters.

Solution 1:1 inch = 2.54 centimeters12 in x 2.54 cm/1 in. = 30.48 cm

Unit Conversion cont.

Example 2: Convert 25 kilograms to grams.

Solution 2:1 kg= 1,000 grams25 kg x 1000 g/1 kg = ____________ g

Example 3:Convert 485 centimeters to meters.

Solution 3: ____________________________________________

Mean, Median, ModeMean: the numerical average. It is calculated by

adding up all the values in a set of data and dividing by the total number of

values.

Median: The middle number in a set of data.

Mode: The number that appears most often in a list

of numbers or data set.

Percent Error Percent Error is a calculation used to determine how

accurate or close to the true value an experimental value really is.

Percent error = Difference between experimental value and true value x

100% true value The ideal percent error is very low, which indicates stronger

accuracy.

Percent Error Example

Sarah measured the length of the board to be 1.32 m. The board’s actual length is 1.25 m.

What was the Sarah’s percent error?

Answer: _____________________________________