UNIT 1 (CHAPTER 2) UNITS OF MEASUREMENT

ACCURACY AND PRECISION (DART BOARD EXAMPLE)

Accuracy- How close you are to the mark you are trying to

hit Closeness of measurements to the correct or

accepted value of the quantity measured.

Precision- How close the measurements are to each other. Closeness of a set of measurements of the

same quantity made in the same way.

Student 1 Student 2 Student 3

10.0 10.4 g 8.1 g

10.1 g 12.3 g 8.0 g

9.9 g 8.4 g 7.9 g

9.8 g 6.2 g 7.8 g

9.7 g 14.1 g 7.7 g

Three students were each asked to prepare 5 samples of sodium chloride crystals that weigh ~10.0 g each. After preparing the samples, each sample was weighed and the following measurements were recorded.

Which set of measurements are the most accurate? The least accurate?Which set of measurements are the most precise? The least precise?

MEASUREMENT ACTIVITY

Using a ruler, measure a small object in centimeters (pen, pencil, book thickness, etc.)

Record your measurement. How certain are you that

_____________is ______________ long? Is it exactly _____________ long or is it a

little more or a little less?

RULE FOR MEASUREMENT

Report measurements to one decimal place past the smallest graduation on the instrument.

If you say someone is 6.0000 feet tall, you are saying that the instrument you are using to measure height can accurately measure to the thousandths place!

WHAT IS THE LENGTH OF THE NAIL?

SIGNIFICANT FIGURES

Rules (from p.47 in the textbook) Zeros appearing between nonzero digits are

significant. Zeros appearing in front of all nonzero digits are not

significant. Zeros at the end of a number and to the right of a

decimal point are significant. Zeros at the end of a number but to the left of a

decimal point may or may not be significant. Zeros as placeholders are not significant. Use a decimal after the zeros if the zeros are considered significant.

HOW MANY SIGNIFICANT FIGURES ARE IN EACH OF THESE MEASUREMENTS? (WORK IN GROUPS)

35.2 m 10.04 g 0.00020 kg 2000 lb 2000. lb 1.25000 m3

SIGNIFICANT FIGURES (P.48-49)

Rules for Rounding- do not follow rules given in Table 6 (too complicated!)

Rules for Addition/ Subtraction with Decimals Answer must have same number of digits to the

right of the decimal place as there are in the measurement having the fewest digits to the right of the decimal point

Rules for Multiplication/ Division Answer can have no more significant figures than

are in the measurement with the fewest number of significant figures

EXAMPLES

5.44m – 2.6103m = 2.83m (2 decimal places)

2.4 g/ml x 15.82 ml = 38g (2 sig figs)

Complete Measurements and Calculations: Significant Figures Worksheets D and E (standard chemistry)

Complete 3-page packet (honors chemistry)

SCIENTIFIC NOTATION & SIGNIFICANT FIGURES

Always put the decimal after the 1st number and using the 4th number, round back to the 3rd number for 3 significant figures.

1400 = 1.40 x 103

.00001256 = 1.26 10-5

UNITS OF MEASURE

SI (Le Système International d’Unités)/ Metric System World’s most widely used system of measurement 7 base units (length, mass, time, temperature,

amount of substance, electric current, luminous intensity- see p.34)

U.S. Customary System (developed from English system)

We need to be able to convert units within each system and between the two systems.

DIMENSIONAL ANALYSIS(UNIT CONVERSIONS)

Conversion factors- Ratios derived from the equality between two different

units that can be used to convert from one unit to the other See Metric Prefixes and Conversion Factors handout

1 ft = 12 in. Write this as 1 ft or 12 in

12 in 1 ft

Convert 78.0 inches to feet.Convert 78.0 inches to centimeters.6.5 feet or ~198 cm

CONVERSION PROCESS

HOW DO I START?

One given: (examples to follow) First step is always to start with the

given/1.

Multiple givens: Try to find a given with no denominator

if possible and start with that given/1

HOW TO GO TO 2ND, 3RD, ETC. STEPS

Each step should cancel out a previous unwanted unit and bring in other units that are progressing toward the desired units of the answer.

5 gallons of water weighs _________ kg? 5 gal 4qt 1L 1000ml 1g 1 kg ------ x ------ x ---------- x ---------- x ------ x ------- = 1 1 gal 1.06qt 1L 1ml 1000g

CALCULATOR USE

The math of the previous problem is most easily handled as a “chain operation”.

All numbers in the numerator are multipliers and all numbers in the denominators are divisors.

Example from previous slide: 5 x 4 / 1.06 x 1000 / 1000 = 18.9

SAMPLE PROBLEM

Express a mass of 5.712 grams in milligrams and in kilograms.

What are the possible conversion factors?

5712 mg0.005712 kg

CLASS WORK

Conversion worksheets (standard) What Am I Eating? (honors)

MASS AND WEIGHT- WHAT IS THE DIFFERENCE?

Mass Measure of the quantity/amount of matter Does not depend on gravity

Weight Measure of the gravitational pull on matter

In space there is no gravity so you are weightless, but you still have the same mass as you do on earth.On other planets with different gravitational pull, you would weight more or less.

DENSITY

Density = Mass Volume

D = m/ V

Densities of common materials given on p.38 in Table 4.

DENSITY PROBLEM

A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum.

What are we given? What are we trying to find? D = m/ V 8.4g = 2.7 g/cm3

3.1 cm3

VARIATIONS ON DENSITY PROBLEMS

Given the density and mass, find the volume.

V = m/ D Given the density and volume, find the

mass. m = D * V

PROBLEM

The volume of a copper wire is 1000 cm3. The density of copper is 8.92g/cm3. What is the mass of the copper wire?

m = D * V 1000 cm3 * 8.92g/cm3 = 8920 cm3

CLASS WORK

Complete Measurements and Calculations: Density worksheet

ADDITIONAL EXAMPLE

Polycarbonate plastic has a density of 1.2 g/cm3. A photo frame is constructed from two 3.0 mm sheets of polycarbonate. Each sheet measures 28 cm by 22 cm. What is the mass of the photo frame?

1.2 g/cm3 x 3.0 m x 1 cm x 28 cm x 22 cm x 2 10 mm

= 440 g

Four Step Process to Solving Problems

PERCENTAGE ERROR

Can be calculated for one experimental/measured data point or a set of data

Compares the experimental value/set of values to the correct or accepted value (given or look up)

% Error = Value experimental – Value accepted x 100%

Value accepted

When would percentage error be negative? Positive?

Sample problem on p.45

HOMEWORK

Complete Measurements and Calculations: Sample Problem C: Percentage Error worksheet

Now we need to know how to write our answers using scientific

notation and the correct number of significant figures.

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Worth its Weight in Gold Activity