Metrics and Measuring

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# Metrics and Measuring - PowerPoint PPT Presentation

Metrics and Measuring. Observations. Types of Observations and Measurements. We make QUALITATIVE observations of reactions — changes in color and physical state. We also make QUANTITATIVE MEASUREMENTS , which involve numbers. Use SI units — based on the metric system. Observations.

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Observations

Types of Observations and Measurements
• We make QUALITATIVE observations of reactions — changes in color and physical state.
• We also make QUANTITATIVE MEASUREMENTS, which involve numbers.
• Use SI units — based on the metric system

Observations

Observations
• Qualitative observations are descriptions of what you observe.
• Example: The substance is a gray solid.
• Quantitative observations are measurements that include both a number and a unit.
• Example: The mass of the substance is 3.42 g.

Metrics

History

The metric system was created to develop a unified, natural, universal system of measurement. In 1790 King Louis XVI of France assigned a group to begin this task. As of 2005, only three countries, the United States, Liberia, and Myanmar, have not changed over to the metric system. The official modern name of the metric system is the International System of Units or abbreviated SI.

The SI system is used universally for all scientific purposes so the metric system will be the only system of measurement we will be using in science this year.

Metrics

Metric System
• A decimal system of measurement whose units are based on multiples of ten

Metrics

Metric Prefixes

The system is easy to use because it is based on multiples of 10

• Kilo (k) = 1000 units
• Hecta (h) = 100 units
• Deka (D) = 10 units
• Base = 1 unit
• Deci (d) = 0.1 unit
• Centi (c) = 0.01 unit
• Milli (m) = 0.001 unit

1 kilogram = 1000 grams

1 liter = 1000 milliliters

1 gram = 1000 milligrams

1 centimeter = 10 millimeters

1 meter = 100 cm

1 kilometer = 1000 meters

Derived and/or Compound Units

The preferred units in science are the

SI base units, shown below. Other units are derived from these seven units.

Physical Quantity Name of Unit Symbol

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Amount of substance mole mol

Electric current ampere A

Luminous intensity candela cd

Derived and/or Compound Units

Derived and Compound Units

Units for other quantities are derived from these seven units. To do this, take the equation used to define the quantity and substitute the appropriate SI base unit.

Example

The volume (V) of cube is given by the length (l) of a side cubed: V = l 3

As the SI unit of length is the meter, the SI unit of volume is the

cubic meter or m3.

Derived Units
• A unit that is defined by a combination of base units
• Volume
• Density

Metrics

Metric Conversion

Kilo Hecta Deka Base Deci Centi Milli

• To convert to a smaller unit, move decimal point to the right or multiply by 10 for each space moved
• Convert 1 Hectameter to decimeters
• Convert 1 Kilometer to meters (base)

Metrics

Metric Conversion

Kilo Hecta Deka Base Deci Centi Milli

• To convert to a larger unit, move decimal point to the left or divide.
• Convert 1 Millimeter to decimeters
• Convert 1 decimeter to Kilometers

Metrics

Metric System

The metric system or International System (SI) is a decimal system of units that uses factors of 10 to express larger or smaller numbers of these units.

Metrics

Units of Length

Examples of equivalent measurements of length:

1 km = 1000 m

1 cm = 0.01 m

1 nm = 10-9 m

100 cm = 1 m

109 nm = 1 m

Metrics

Length
• The distance from one point to another
• Meter (m) – the SI unit of length
• Tool used to measure length depends on the size of the object
• Larger objects (the room)
• meter stick
• Smaller objects (pencil length)
• centimeter ruler

Metrics

Measuring Area
• Area = Length x Width

The square has an area of 4 square

centimeters (4 cm2)

1 cm

Area = l x l2

1 cm

= 2 cm x 2 cm

Area = 4 square centimeters (4 cm2)

2 cm

2 cm

Metrics

Mass
• The SI unit for mass is the kilogram (kg)
• The gram is the base unit
• mass of vitamins or medicines are so small that we use milligrams (mg)

Metrics

Weight (Force times Mass)
• Measure of the force of gravity acting on the mass of an object (kg  m / s2)
• SI unit is the Newton (N)
• Weight can change (since gravity can change).
• Mass does not!

Metrics

Volume
• The amount of space a substance takes up
• Volume of a liquid is found using a graduated cylinder
• Unit is liters (L) or milliliters (mL)

Frequently used SI units

1 milliliter (mL) = 1 cubic

centimeter (cc) or (cm3)

1 liter (L) = 1000 milliliters (mL)

or 1 dm3

Metrics

Measuring Volume
• Liquid volume measured using graduated cylinder
• Read volume at meniscus (downward curve of water)
• What is the volume of this liquid?

Metrics

Measuring Volume
• Find the volume of these liquids

15.0 mL

16.0 mL

12.5 mL

Metrics

Volume
• Volume of a solid is found using the volume equation
• length x width x height
• In this equation, we are also multiplying the units together so units for the volume of a solid are…
• m x m x m = m3 OR cm x cm x cm = cm3
• Also know that 1 mL = 1 cm3 = 1 cc (cubic centimeter)
Units of Volume

1 m3 (1003 cm3)/(1 m3) = 1,000,000 cm3

1,000,000 cm3 = 1  106 cm3

Metrics

Measuring Volume
• Calculate the volume of the box

6 mm

2 mm

5 mm

Volume =

l x w x h

Volume =

6 mm X 5 mm X 2 mm

Volume =

60mm3

Metrics

Water Displacement
• Some solid samples, such as an irregularly shaped rock cannot have their volume measured easily by using the volume equation (length x width x height)
• For these solids, scientists use a technique called Water Displacement

Metrics

Water Displacement

1.Add water to a graduated cylinder and record its volume (ex: 7 ml)

2.Place the irregularly shaped solid into the graduated cylinder already containing water and record the new volume (ex: 9 ml)

Metrics

Water Displacement

3.Subtract the smaller volume from the larger volume (water only) to get the volume of the irregularly shaped solid. (ex: 9 ml – 7 ml = 2 ml)

4.The irregularly shaped solid takes up 2 ml of space. Since it is a solid, we need to state the volume using cm3 so we would say that its volume is 2 cm3

Metrics

There is one special case in metrics that ties mass with volume.

One gram of water, at temperature 4 °C is equal to one milliliter of water which is equal to one cm3 of water.

1 g H2O = 1 mL H2O = 1 cm3 H2O

If one milliliter of water equals one gram of water then 1000 milliliters of water or 1 liter of water equals 1000 grams or 1 kilogram of water.

1 gram of water

kilogram/liter

Metrics

Density
• Amount of mass in a given volume
• Kg/m3 or g/cm3
• Density = mass

volume

• Water has a density of 1g/cm3

Metrics

Time
• The period between 2 events
• The SI unit of time is the second (s)
• Measurement tool of time is a stopwatch

Metrics

Temperature
• Measure of the energy of motion of particles in a substance
• Kelvin (K) is the SI unit of measurement in the metric system
• Celsius is used for experimentation since a degree Kelvin is the same as a degree Celsius

Metrics

Thermal Energy and Temperature
• Thermal energy is a form of energy associated with the motion of small particles of matter.
• Temperature is a measure of the intensity of the thermal energy (or how hot a system is).
• Heat is the flow of energy from a region of higher temperature to a region of lower temperature.

Metrics

Anders Celsius

1701-1744

Lord Kelvin

(William Thomson)

1824-1907

Temperature Scales
• Fahrenheit
• Celsius
• Kelvin

Metrics

212 ˚F

100 ˚C

373 K

100 K

180˚F

100˚C

32 ˚F

0 ˚C

273 K

Temperature Scales

Fahrenheit

Celsius

Kelvin

Boiling point of water

Freezing point of water

Notice that 1 kelvin = 1 degree Celsius

Measuring

Measurements:

Every measurement has UNITS.

Every measurement has UNCERTAINTY.

Measuring

Nature of Measurement

Measurement

• Quantitative observation consisting of two parts.
• number
• scale (unit)
• Examples
• 20 grams
• 6.63 × 10–34 joule·seconds

Measuring

• A digit that must be estimated is called uncertain.
• A measurement always has some degree of uncertainty.
• Record the certain digits and the first uncertain digit (the estimated number).

Measuring

Measurement of Volume Using a Buret
• The volume is read at the bottom of the liquid curve (meniscus).
• Meniscus of the liquid occurs at about 20.15 mL.
• Certain digits: 20.1
• uncertain digit: 20.15

Measuring

Precision and Accuracy

Accuracy

• Agreement of a particular value with the true value.

Precision

• Degree of agreement among several measurements of the same quantity.

Measuring

Significant Figures
• Non-zero numbers are always significant.
• Zeros between non-zero numbers are always significant.
• Zeros before the first non-zero digit are not significant. (Example: 0.0003 has one significant figure.)
• Zeros at the end of the number after a decimal place are significant.
• Zeros at the end of a number before a decimal place are ambiguous (e.g. 10,300 g).

Measuring

Significant Figures & Calculations

Line up the numbers at the decimal point and the answer cannot have more decimal places than the measurement with the fewest number of decimal places.

Multiplication and Division

The answer cannot have more significant figures than the measurement with the fewest number of significant figures.

Measuring

Rules for Counting Significant Figures

1. Nonzero integers always count as significant figures.

• 3456 has 4 sig figs (significant figures).

Measuring

Rules for Counting Significant Figures
• There are three classes of zeros.

a. Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures.

• 0.048 has 2 sig figs.

Measuring

Rules for Counting Significant Figures

b. Captive zeros are zeros between nonzero digits. These always count as significant figures.

• 16.07 has 4 sig figs.
Rules for Counting Significant Figures

c. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point.

• 9.300 has 4 sig figs.
• 150 has 2 sig figs.

Measuring

Significant Figures in Mathematical Operations

1. For multiplication or division, the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation.

1.342 × 5.5 = 7.381  7.4

Measuring

Significant Figures in Mathematical Operations

2. For addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation.

Measuring

Rules for Counting Significant Figures

3. Exact numbers have an infinite number of significant figures.

• 1 inch = 2.54 cm, exactly.
• 9 pencils (obtained by counting).

Measuring

Concept Check

You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred).

How would you write the number describing the total volume?

Measuring

Concept Check

The volume in the left cylinder is:

2 is certain

2.8 is the estimated uncertain digit

because the smallest lines are in twos, not ones, and so any measurement is a guess.

If the smallest lines were by ones, then the estimated uncertain digit would be in the hundredths rather than the tenths as above.

Measuring

Concept Check

The volume in the right cylinder is:

0.2 is certain

0.28 is the estimated uncertain digit

because the smallest lines are in two-tenths, not one-tenths, and so any measurement is a guess.

If the smallest lines were by one-tenths, then the estimated uncertain digit would be in the thousandths rather than the hundredths as above.

Measuring

Concept Check

Therefore the total combined volume of the two liquids would be:

2.8

+ 0.28

3.08

Rounded for the Rules of Adding Significant Digits

3.1

Measuring

Always estimate ONE place past the smallest mark!

Measuring

Measurement and Uncertainty

The last digit in any measurement is an estimate.

uncert

estimate

a. 21.2°C

certain

b. 22.0°C

• 22.11°C WRONG
• 22.1°C RIGHT

Measuring

What is volume of the fluid in the graduated cylinder?

1) 17 mL

2) 17.5 mL

3) 17.70 mL

4) 15.25 mL

Measuring

What is volume of the fluid in the graduated cylinder?

1) 17 mL

2) 17.5 mL

3) 17.70 mL

4) 15.25 mL

Measuring

cm

What is the length of the dark line?

1) 1.6 cm

2) 1.67 cm

3) 2 cm

4) 1.660 cm

Measuring

cm

What is the length of the dark line?

1) 1.6 cm

2) 1.67 cm

3) 2 cm

4) 1.660 cm

Measuring

What is the length of the wooden stick?

1) 4.5 cm

2) 4.54 cm

3) 4.547 cm

4) 4.0 cm

Measuring

What is the length of the wooden stick?

1) 4.5 cm

2) 4.54 cm

3) 4.547 cm

4) 4.0 cm

Measuring

What is the length of the pencil?

1) 3.21 cm

2) 8.00 cm

3) 3.2 cm

4) 8.0 cm

Measuring

What is the length of the pencil?

1) 3.21 cm

2) 8.00 cm

3) 3.2 cm

4) 8.0 cm