K (what do you know W (what do L (what About Measurement) you want to have

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learned) about Measurement

KWL STRATEGY

CH. 2 Precision & Accuracy ,% error, Metrics,

Measurement & Significant Figures

In the context of the scientific method, precision and accuracy have two distinctly different meanings.

The accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual (true)value.

The precision of a measurement system is the degree to which repeated measurements under unchanged conditions show the same results.

See dartboard (p. 44) A measurement system can be accurate but not precise,

precise but not accurate, neither, or both.

Precision vs. Accuracy

Visualizing the concept

www.yorku.ca/psycho/en/pics_en/postscript_f1.gif

% error = measured – accepted accepted X

100

p. 45 #1 practice problemFind the % error if a mass measurement is

17.7 grams when the correct mass is 21.2 grams.

CALCULATING % ERROR

A liquid’s volume is measured in a beaker as 40 mL. It is then measured in a graduated cylinder as 45.5 mL. Find the % error.

Example 2

P. 45 # 1—2

p. 60 #35—37

1. 0.9%2. 0.4%3. 3.5%4. 9.3%5. 1.7%6. 3.7%7. 0.3%8. 10.4%

% error problems

MEASUREMENT WARM UP 1. Based on the following data collected,

comment on this person’s accuracy & precision: ***Volume in beaker trial 1= 30.0 mL

Trial 2 = 31.0 Trial 3= 31. 5

***Volume in cylinder = 45.5 mL 2. Calculate % error: A student measures mass as 50.9 grams.

The instructor measures 55.9 grams.

1. high precision; low accuracy 2. 8.9%

Write a paragraph to your friend explaining to him or her the difference between accuracy vs. precision. Include an example using the dartboard analogy. (refer to p. 44 if needed)

WRITING ACTIVITY--ACTIVATOR

CALCULATE % ERROR FOR THE FOLLOWING:1. A student measures the volume of a cube to be 20.5 cubic

centimeters. He checks this against the correct volume which is 25 cubic centimeters.

2. A liquid’s volume is 35 mL in a graduated cylinder, while in a beaker the volume is 25 mL.

3. CommentOn precision And accuracyFor picture D.

QUIZ

http://www.brookscole.com/math_d/special_features/ext/internet_activities/matovina/metric

ONLY COMPLETE 1—6 and #8 TODAY USE YOUR OWN NOTEBOOK PAPER

IPAD ACTIVITY—Introduction to Metrics

Why is the metric system of measurement (which uses meters, liters, grams, etc.) preferred AND easier to use rather than the English system of measurement (which uses pounds, feet, etc.)?

ACTIVATOR:

1 foot. = 12 inches 1 pound = 16 ounces 1 cup = 8 ounces 1 yard = 3 feet 1 mile = 5280 feet

ENGLISH SYSTEM UNITS:

Also known as the SI based system (International System of Measurements)

It is more preferred rather than the English system of measurements because it is based on units of 10.

Measurement systems are all based on “standards” which are physical representations for each measurement unit.

We will learn about the prefixes “Tera” through “pico”. (see chart)

METRIC SYSTEM

Mass = gramDistance = meterVolume = liters or cubic meterTime = secondsTemperature = KelvinAmount of a substance = moleElectric current = ampereLight intensity = candelaArea = square meterEnergy = joule

METRIC QUANTITIES AND WHAT UNITS THEY ARE MEASURED IN:(see p. 34 in your textbook)

1 KILOmeter = ________________meters

1 CENTIgram = ______________________grams

1 millisecond = __________________seconds

ADDING PREFIXES TO BASE UNITS

THE METRIC LINE(STAIRCASE)

THE GREAT MIGHTY king henry died by drinking chocolate milk maybe not pasteurized

METRIC ACRONYM

mg

kL

Mm

mm

um

m

TELL WHAT EACH SYMBOL STANDS FOR:

METRIC CONVERSIONS

Name 3 basic metric units.Name 2 prefixes AND give their symbol.Name 1 thing you know about a “standard” of

measurement.

ACTIVATOR: 3-2-1

1. liquids—graduated cylinder (measures in mL)

2. rectangular shaped solids- use a ruler for length x width x height (measured in cubic

cm or cm3 or cc)3. Irregular shaped solids—water displacement

***VOLUME—the amount of space something takes up

3 ways for measuring volume:

25 mL = ___________________cc (cm3)

25 cc = ________________________L

YOU TRY:

1—12, 15, 16

METRIC HANDOUT

Describe how you would take the volume of a glass of water, a rectangular block, and a marble. Also, tell what units that you would use to measure each.

SUMMARIZER:

WRITING ASSIGNMENT: (1-2 paragraphs) Discuss the differences between area &

volume. Include in your discussion: ways they are measured, units which they are measured in, and tools used to measure them. Also, remember the different methods for measuring volume.

% ERROR/METRICS 1. A lab tech measures the boiling point

of water to be 99.5 C. The true boiling pt of water is 100.0 C. Calculate the % error. (SHOW WORK!!)

2. 0.0075 g = ______________________ng 3. 3400 kg = ____________________Mg 4. 258 daL = _______________________mL 5. 534 L = __________________cm3

Warm up

1. 99.5 – 100.0 x 100 = 0.5%100.0

2. 7 500 000 ng3. 3.4 Mg4. 2 580 000 mL5. 534 000 cc (mL)

In a paragraph, describe how mass, volume, length, and temperature are measured.

ACTIVATOR

PART III #8 SHOW WORK FOR % ERROR

Accepted values:Bottle = 7.095 gramsClamp = 75.069 gramsDomino = 5.371 gramsStopper = 7.090 grams

LAB—UNCERTAINTY OF MEASUREMENT

METRIC WARMUP GIVE THE SYMBOL FOR EACH UNIT: 1. Micrometer 4. Megameter 2. Meter 5. millimeter 3. Kiloliter WHAT QUANTITY DO THESE UNITS MEASURE? 7. meter 10. gram 8. cc 11. Cm3

9. liter 12. Square meter PERFORM THESE METRIC CONVERSIONS: 13. 2.67 ng = _______________pg 14. 34000 m = ______________Mm 15. 50 cc =_______________mL 16. 3 L = __________________cm3

This is done when BOTH units have the SAME exponent (squared to squared or cubed to cubed)

Ex: 100 cm2 = _______________m2

cm to m is normally 2 spaces left, so multiply this 2 spaces x the exponent of 2 = total of 4 spaces left

Ex: 0.0075 Mm3 = ________________km3

Mm to km is normally 3 spaces right, so multiply by exponent of 3 = 9 spaces right

CONVERSIONS INVOLVING EXPONENTS

1. 55 cc = ______L 2. 0.00035 Mm = _________m 3. 675 dL =____________kL 4. What do millimeters measure? 5. What do kilograms measure? 6. What do liters measure? 7. What do cubic millimeters measure? 8. What do square centimeters measure? 9. Which is larger: 250 cc or 0.5 L? 10. Find the area of a box measuring 5 cm by 8 cm. 11. Does milli make the base unit larger or smaller? 12. Find the volume of a rock that’s dropped in 25 mL of

water and the level then rises to 38 mL.

FINAL METRIC WARMUP

1. 0.055 L 2. 350 m 3. 0.0675 kL 4. length 5. mass 6. volume 7. volume 8. area 9. 0.25 L or 0.5 L 10. 5 cm x 8 cm = 40 cm2

11. smaller 12. 38 – 25 = 13 mL

BOOK PROBLEMS (% error, metrics, accuracy/precision)

p. 59 #1, 4, 7, 8 ab, 9 ab, 16, 20, 21, 24, 25, 37

p. 63 #1, 3, 4, 6, 7, 8

Explain why error always exists in measurement.

ACTIVATOR

Significant figures help scientists be able to do the same thing when taking measurements and doing calculations.

SEE P. 46

Significant Figures

1. Digits from 1-9 are always significant. 2. Zeros between two other significant

digits are always significant 3. Final zeros to the right of the decimal

place are significant. 4. Zeros used solely for spacing the

decimal point (placeholders) are not significant (Unless specifically measured and noted with a line above the number).

Sig Fig Rules

The letters "A" (decimal absent) and "P" (decimal present) correspond to the "Atlantic" and "Pacific" Oceans on a map. 

HOW TO DETERMINE THE NUMBER OF SIG FIGS---p. 47

Now, imagine an arrow being drawn from the appropriate coast.  Once the arrow hits a NONZERO digit, this digit and all of the digits after it are significant.

Example 1.  How many significant digits are shown in the number 20 400 ?  Well, there is no decimal, so we think of "A" for "Absent".  This means that we imagine an arrow coming in from the Atlantic ocean

20 400 this shows 3 significant numbersas you do not count numbers

until you hit a significant digit

Decimal Absent

Modified from http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm

Example 2.  How many significant digits are shown in the number 0.090 ?  Well, there is a decimal, so we think of "P" for "Present".  This means that we imagine an arrow coming in from the Pacific ocean.

0.090 This shows that the number has two significant digits after the non

zero number is encountered

Decimal Present

Modified from http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm

1. 2300. m 2. 2300 g 3. 0.005 L 4. 23.92 sec 5. 40,060 kg 6. 2005 moles 7. 32.00 Kelvin 8. 43.090 Mm

NOW YOU TRY…….First decide if A or P??HOW MANY SIG FIGS IN EACH?

1. P = 4 2. A= 2 3. P = 1 4. P = 4 5. A = 4 6. A = 4 7. P = 4 8. P = 5

TELL IF THE FOLLOWING ARE “ATLANTIC” OR “PACIFIC” AND THEN TELL HOW MANY SIG FIGS:

1. 0.0035 cm 7. 0.004 mg 2. 10.00 g 8. 549000 cm 3. 3400 m 9. 3000 g 4. 53.57 mm 10. 0.45670 nm 5. 40600 kg 11. 2734 km 6. 200.040 Mm 12. 5.070 sec

TELL IF THE FOLLOWING ARE “ATLANTIC” OR “PACIFIC” AND THEN TELL HOW MANY SIG FIGS:

1. 67. 930 g 2. 2600 m 3. 0.0070 km 4. 5030 cm 5. 67.00 mm 6. 3.69 sec 7. 0.03 mm 8. 1000 kg 9. 1000. Mm 10. 63.500 kg

QUIZ—COPY THE PROBLEM

You may ONLY do this to zeros in ATLANTIC numbers

1. put a bar over the zero 2500—has 2 sig figsHow to make 3 sig figs??How to make 4 sig figs??

2. Put a decimal at the end (making it a pacific #)25002500.

HOW TO MAKE ZEROS SIGNIFICANT WHEN THEY’RE NOT ALREADY

TELL HOW MANY SIG FIGS IN EACH: (1ST DECIDE IF A or P) 1. 21.34 g 10. 51.200 g 2. 52.340 g 11. 6050 m 3. 28,007 L 12. 2000 L 4. 80.00 m 13. 40.50 cm 5. 0.0025 g 14. 0.192 m 6. 23,000 cm 15. 3000. L 7. 28, 875 mm 16. 30 mm 8. 505,100 g 17. 30,650 Mm 9. 0.050 L 18. 0.00500 g

Problems involving Lines over zeros—1st decide if A or P??

1. 4 11. 3 2. 5 12. 3. 5 4. 4 5. 2 6. 5 7. 5 8. 5 9. 2 10. 5

When trying to do this, move through the number from left to right.

Ex: Round to 1 sig fig:

2300

0.0897

5.9

ROUNDING TO A CERTAIN NUMBER OF SIG FIGS

Round to 2 sig figs: 2895

0.0956

Round to 3 sig figs:2895

0.6

TELL HOW MANY SIG FIGS ARE IN EACH--1st decide if A or P:

1. 0.00306 5. 3000. 9. 2.0 2. 0.003060 6. 43.06 3. 4300 7. 3.020 4. 4060 8. 5000 ROUND EACH TO 2 SIG FIGS: 1. 0.0357 4. 657 2. 2350 5. 0.0695 3. 90.34 6. 0.7 ROUND EACH TO 1 SIG FIG: 1. 3693. 0.0078 2. 20.47 4. 379.5

WARM UP

1. 3 5. 4 9. 2 2. 4 6. 4 3. 2 7. 4 4. 4 8. 1

1. 0.036 4. 660 2. 2400 5. 0.070 3. 90.6. 0.70

1. 400 2. 20 3. 0.008 4. 400

Round answer to the FEWEST DECIMAL PLACES that are in the problem

10.711 g 4 mL 5.75 cm+3.23 g -3.4 mL +2.976 cm

Add/Substract with Sig Figs

1. 13.941 = round to 2 dec. = 13.94 g 2. 0.6 = round to 0 dec. = 1 mL 3. 8.726 = round to 2 dec. = 8.73 cm

Round answer to the FEWEST SIG FIGS that are in the problem

2.32 cm x 77.96 cm =

62.0 g / 2.000 mL =

1.805 m x 6.0 m =

Multiply/Divide with Sig Figs

1. 180.8672=round to 3 sig figs = 181 cm2

2. 31=round to 3 sig figs = 31.0 g/mL

3. 10.83= round to 2 sig figs = 11m2

Give any 3 measurements and tell how many sig figs are in each.

Describe the 2 different ways to round (add/subtract VS. Multiply/divide)

Name 1 way to make zeros significant when they’re not to begin with.

SUMMARIZER 3-2-1

1—34 EVEN

HOMEWORK—SIG FIGS HANDOUT

22. 30.647 = 30.6 grams 24. 9.2946 = 9.29 L 26. 29.56 = 30 sec 28. 1.967 = 2 g/mL 30. 0.022737 = 0.023 sq inches 32. 0.25 = 0. 250 kg/L 34. 0.012049 = 0.01205 Mm2

1. 5.0 m X 457 m=2. 16.56 g + 13 g =3. 5.60 g / 22.4 L =4. 0.059 g / 0.03 L =5. 14.26 cm - 4.9654 cm =

WARM UP

2285 = round to 2 sig figs = 2300 m2

29.56 = round to no decimal places = 30 g

0.25 = round to 3 sig figs = 0.250 g/L 1.966666 = round to 1 sig fig = 2 g/mL 9.2946 =round to 2decimal places = 9.29

cm

ANSWERS

P. 50 #1—3

P. 57 #3—4

Why would someone want to put a measurement into scientific notation?

ACTIVATOR

Reduces the number of zeros in really big or really small numbers

The number in front determines the number of sig figs

Starting out, the decimal MUST be written to the right of the first nonzero number in order to be in correct scientific form; then, depending on the exponent, it can be moved left or right to convert to a regular number.

5.64 x 104 (correct form with 3 sig figs)0.0035 x 102 (incorrect form) Why??340 x 103 (incorrect form) Why??

SCIENTIFIC NOTATION

6.023 x 1023 4 sig figs

6.67 x 10-11 3 sig figs

2.00 x 10-3 3 sig figs

Other examples of Correct Form

In your calculator, 3.05 x 109 may appear:

3.05 E9

3.05 EE 9

3.05 9

If the exponent is POSITIVE, move decimal that many places to the RIGHT.

Ex: 3.450 x 103

***Remember to keep SIG FIGS the same!! If the exponent is NEGATIVE, move decimal

that many places to the LEFT. Ex: 6.090 x 10-3

***Remember to keep SIG FIGS the same!!

Converting from Scientific Notation to Regular Number (Standard Form)

1. 4.560 x 105 = 2. 3.9 x 10-3 =

3. 5.0 x 100 =

YOU TRY:

Remember that the decimal must be moved to the right of the first nonzero digit. Also, remember to keep SIG FIGS the same.

If the number is greater than 1 to start with, use a positive exponent.

Ex: 305,000

If the number is less than 1 to start with, use a negative exponent.

Ex:0.004060

CONVERTING INTO SCIENTIFIC NOTATION:

1. 456,000. =

2. 0.003400 =

3. 67000 =

YOU TRY:

SIG FIGS---EVEN (OPTIONAL)

SCIENTIFIC NOTATION--EVEN

SIG FIGS/SCIENTIFIC NOTATION HANDOUT

WARM UP PUT INTO SCIENTIFIC NOTATION: 1. 0.0060 2. 23500 PUT INTO STANDARD FORM (REGULAR

NUMBER) 3. 3.50 X 102

4. 6.788 X 10-3

P. 57 #6

P. 60 #43—45

p. 48 #1-2 p. 57 #1-3 p. 60 #29, 38 p. 31 #2 p. 42 #1-3 p. 59 #6-9, 16, 20, 21, 23, 25a, 38, 50, 51

Accuracy, Metric, and Sig Figs

WHAT TO STUDY FOR MEASUREMENT TEST 1. Qualitative vs. quantitative measurement 2. What’s the purpose of a standard in measurement 3. Basic units for length, time, volume, mass, and temp. 4. Metric prefix symbols, numerical meanings, and

exponent meanings 5. Metric conversions (normal, cc = mL, and exponent

ones) 6. Units for area and volume 7. 3 ways to measure volume 8. % error 9. Accuracy vs. precision 10. Mass vs. weight 11. Counting # of sig figs AND calculation rules for sig

figs 12. Scientific notation into standard form (and vice-versa) 13. Vocabulary sheet 14. Reading metric tools 15. Measurement video ?s