NOTES: MEASUREMENT AND SIGNIFICANT DIGITS



Unit 1B NOTES: MEASUREMENT of MATTER

Types of Measurements

a. Quantitative Measurement –is a measurement that includes a number and a unit (a quantity)

Examples: 44 grams, 25 ml, 5 books.

b. Qualitative Measurement – is a verbal description of a substance (a quality)

Examples: round, hot

Practice

Directions: Determine which of the following statements are qualitative or quantitative observations. Place a capital L on the lines in front of the statements that are qualitative observations. Place a capital N on the lines in front of the statements that are quantitative observations. If both, write both.

____ 1. Kim observed six red objects in a basket.

____ 2. Ricky determined the objects in the basket have a circumference of ten centimeters.

____ 3. Ian measured an object to have a mass of 23.5 grams.

____ 4. The object has a black shiny surface.

____ 5. The thermometer indicates that the liquid has a temperature of 320C.

____ 6. Billy observed 3 green geckos sitting on a tree branch.

____ 7. Jake recorded into his journal that the blue block floated lower in the

water than the red block.

____ 8. The earth material has a density of 3.2 g/cm3.

____ 9. The mineral is greenish-blue in color.

____ 10. This morning, the temperature was 420F.

Units of Measurement

SI unit – an international system of units

Base Unit – need only one measurement

Derived Unit – a combination of 2 or more base units

UNITS

Base Units Derived Units

• independent of

ex. Mass, Time ex. Volume (l x w x h), Density (m/v)

|Quantity |Definition |Typical Unit | SI Unit |Base unit (B) |Equipment |

| | | | |or | |

| | | | |Derived unit | |

| | | | |(D) | |

|Mass |Measure of the amount of _____________ | | | | |

| | | | | | |

|Volume |Measure of the | | | | |

| |____________ that matter takes up | | | | |

|Density | | | | | |

| | | | | | |

|Length |________________ | | | | |

| |between two points | | | | |

|Time |Duration of an event | | | | |

| | | | | | |

|Temperature |Measure of ___________________ | | | | |

| |(vibration of molecules) | | | | |

Temperature

Remember: 1) Temperature is a measure of kinetic energy (the energy of movement or vibration of particles). 2) Energy is the ability to do work and is measured in the units Joules or Calories

Kelvin, Celsius, and Farenheit Temperature Scales

Units of temperature:

Kelvin (K)

Degrees Celsius (°C)

Degrees Farenheit (°F)

Celsius temperature scale: At 0°C water freezes. At 100°C water boils

Kelvin temperature scale: 0 K is the lowest temperature on the Kelvin scale; it is also called Absolute zero.

There are no negative values on the Kelvin scale.

Absolute zero: The temperature at which everything stops moving (vibrating).

Practice

1) Make the following conversions between units of temperature:

a. 25ºC to Kelvin d. 355K to Celsius

b. 149 ºC to Kelvin e. 408K to Celsius

2) Temperature facts:

1. The highest recorded temperature in the world was recorded in El Azizia, Libya, in September, 1922. The recorded temperature was 136ºF, or 58ºC. Report this temperature in Kelvin.

2. The lowest recorded temperature in the world was recorded in Vostock, Antartica in July, 1983. The recorded temperature was -129ºF, or -89ºC. Report this temperature in Kelvin.

Precision and Accuracy of Measurements

What is the difference between an accurate measurement and a precise measurement?

Equipment can only be precise. Humans can be precise and/or accurate.

Practice

1. Consider the data obtained for the length of an object as measured by three students (A, B, and C). The length is known to be 14.54 cm. Which student has done the most precise determination?

|Trial 1 |Trial 2 |Trial 3 |Trial 4 |Trial 5 |

|14.7 |14.8 |14.9 |14.8 |14.8 |

|14.8 |14.2 |14.5 |14.7 |14.3 |

|14.3 |14.2 |14.8 |14.9 |14.8 |

a) Student A has done the most precise work.

b) Student B has done the most precise work.

c) Student C has done the most precise work.

2. The term that indicates the reproducibility of a measurement is:

a) Qualitative

b) Precision

c) Accuracy

d) Quantitative

3. A crucible is known to have a mass of 24.3162 g. Students A, B, and C determine the mass of the crucible by repeated measurements. Which student has done the most accurate determination?

|Trial 1 |Trial 2 |Trial 3 |Trial 4 |Trial 5 |

|24.8 |24.0 |24.2 |24.1 |24.3 |

|24.5 |24.3 |24.5 |24.4 |24.3 |

|24.8 |24.9 |24.8 |24.9 |24.8 |

a) Student A has done the most accurate work.

b) Student B has done the most accurate work.

c) Student C has done the most accurate work.

Metric Unit Abbreviations

Write the correct abbreviation for each metric unit.

1) Kilogram _______ 4) Milliliter ________ 7) Kilometer ______

2) Meter ______ 5) Millimeter _______ 8) Centimeter _______

3) Gram ______ 6) Liter _______ 9) Milligram _______

Uncertainty in Measurements

Reading lab equipment / Significant digits

These 3 graduated cylinders have different levels of precision.

• One measures 4 ml

• One measures 4.3 ml

• One measures 4.35 ml

Therefore, graduated cylinder #_______ gives us the most precise measurement.

Significant digits: All of the digits that are known plus the last digit which is estimated; these are the significant figures

Instruments differ in the number of significant figures which can be obtained from their use and therefore, the precision of the measurements.

Practice Record the measurements.

[pic]

Dimensional Analysis

• Dimensional analysis is a way of problem solving to convert between units using conversion factors

• A conversion factor = a ratio of equivalent values used to express the same quantity in different units.

(ex.) 1 foot = 12 inches, so the conversion factor is 1 foot or 12 inches

12 inches 1 foot

(ex.) 16 ounces = 1 pound, so the conversion factor is 16 ounces or 1 pound

1 pound 16 ounces

(ex.) 3 feet = 1 yard, so the conversion factor is 3 feet or 1 yard

1 yard 3 feet

Example: Convert 2 miles to inches. (This example is a two-step process)

Solve problems a., b., and c. using the following conversion factors:

1 picket = 3 stangs 2 ibbles = 5 dobs 7 noggins = 4 loobs

a. 7 stags = ____________ pickets c. 3.5 dobs = _____________ ibbles

b. 5 noggins = ____________ loobs

Practice B: Real conversions that require only one conversion factor (one step)

Real Conversion factors:

2.54 cm = 1 inch 1 mile = 5280 feet 1 gallon = 4 quarts

3.79 L = 1 gallon 454 g = 1 pound

16 ounces = 1 pound 1 calorie = 4.18 Joules

1 mL = 1 cm3 1 mole = 6.02 X 1023 atoms

a. 5.7 inches = _____________ cm b. 85 ounces = ________________ pounds

c. 125 grams = ______________ pounds d. 72 cm3 = ______________ mL

e. 2.5 miles = ______________ feet f. 4 moles = ________________ atoms

g. 24 Joules = ____________ calories h. 6 gallons = _________________ liters

i. 45 grams = ___________________ pounds

Practice A: Real conversions that require more than one conversion factor (two steps). Use real conversion factors.

j. 2.75 feet = _________________ cm

k. 38 quarts = __________________ liters l. 15 gallons = ________________ M

Practice A

Bill has a farm where he grows corn. He goes to the local farmers market to exchange 1,000 ears of corn for food for his family. The farmers market has set up these items and their trade value:

3 ears of corn = 2 peaches

10 apples = 3 watermelons

4 peaches = 3 apples

15 watermelons = 1 chicken

8 chickens = 1 cow

1. How many ears of corn would it cost to get 30 peaches?

2. How many watermelons could he buy with 300 chickens?

3. How many apples could you get with 15 chickens?

4. How many watermelons could you get with 250 ears of corn?

5. With 1,000 ears of corn, does Bill have enough to buy a cow? Prove it!

6. Are there any leftover ears of corn if he can get a cow? If so, can he get any chickens with them? If so, how many?

Metric Conversions Using the Ladder Method

Try these conversions, using the ladder method.

1000 mg = _______________ g 1 L = ________________ mL

160 cm = _______________mm 14 km = ______________m

109 g = _________________ kg 259 m = ______________km

Practice: Try these conversions, using the ladder method.

1) 2000 mg = ________ g 6) 5 L = __________ mL 11) 16 cm = _______ mm

2) 104 km = _________ m 7) 198 g = ________ kg 12) 2500 m = ______ km

3) 480 cm = _________ m 8) 75 mL = _______ L 13) 65 g = _________ mg

4) 5.6 kg = __________ g 9) 50 cm = _______ m 14 ) 6.3 = _________ mm

5) 8 mm = __________ cm 10) 5.6 m = ______ cm 15) 120 mg = _______ g

Compare, using , or = .

16) 17) 18)

19) 20) 21)

Make the following conversions:

1) 3.4 milliliters 6) 45 meters to centimeters

2) 876 milliliters to meters 7) 11.7 grams to kilograms

3) 78,999 milligrams 8) 0.0009 kiloliters to liters

4) 0.9 centigrams to grams 9) 44 centimeters to meters

5) 112 meters to milliliters 10) 277 kilograms to grams

Metric Conversions Using Dimensional Analysis:

1,000,000 micro_____ = 1 _________ 1,000,000 µg = 1g 1,000,000 µL = 1 L

1,000 milli _____ = 1 _________ 1,000mg = 1 g 1,000mL = 1 L

100 centi _____ = 1 _________ 100cg = 1 g 100cL = 1 L

10 deci _____ = 1 _________ 10dg = 1 g 10dL = 1 L

1 kilo _____ = 1,000 ______ 1 kg = 1,000g 1 kL = 1,000 L

METRIC CONVERSIONS USING DIMENSIONAL ANALYSIS:

CONVERSION RULES (using chart on p.11)

• Left is Larger

• If you see one letter (ex) g, L, m, then you are in "UNIT."

• The prefixes are always attached to a standard unit.

• This system is based on Powers of 10 so prefixes that are…….

…… 2 moves away are 100x larger.

(left)

…… 3 moves away are 1000 x larger.

(left)

Practice: Make the following metric conversion using dimensional analysis:

a. 150cg = _____________ g b. 28km = ___________________ m

c. 5.0m = ________________ dm d. 125µg = __________________cg

e. 25 kJ = _______________d J f. 10dsec = ________________ msec

Sometimes you have 2 units to convert in the same measurement.

HANDLE 1 UNIT AT A TIME!!!

(ex) 29 cm / s → ? Km / h

(ex) 23 Km / h → ? µm / s

Density

| | | |

| | | |

| |[pic] | |

|[pic] | |[pic] |

Density = Mass /Volume or D = m/V

1. Calculating density with known mass and volume:

a. determine the density of a material that has a mass of 36g and volume of 2.5 cm3.

b. find the density of a 25g object that displaces 7.5mL of water. (1 mL = 1 cm3)

2. Calculating volume with known mass and density:

V = m/D

a. find the volume of 50g of olive oil if the density of olive oil is 0.80g/mL.

b. find the volume of 25.0g of gold if the density of gold is 19 g/cm3.

3. Calculating mass with known density and volume:

m = V x D

Find the mass of a 3.5 cm3 bar of gold. (density is 19 g/cm3)

4. Density is a physical property. It can be used to help identify a substance. Example: the density of aluminum is 2.7g/cm3. A 20.0g metal rod displaces 4.5mL of water. Is the rod aluminum? (1 mL = 1 cm3).

Density Problems Worksheet Period _____ Date _________________

Complete the following density problems.

• SHOW ALL WORK!!

• Include the PROPER UNITS in your final answers.

1. The density of lead is 11.4 g/cm3. What is the mass of a piece of lead that has a volume of 19cm3?

2. What is the volume of a sample of cough syrup that has a mass of 50.0 g? Then density of cough syrup is

0.95 g/cm3.

3. Aspirin has a density of 1.40 g/cm3. What is the mass of a 25.0 mL sample of aspirin? (1 mL = 1 cm3)

4. A cup of gold colored metal beads was measured to have a mass 425 g. By water displacement, the volume of the beads was calculated to be 48.0 mL. Given the following densities, Gold: 19.3 g/ cm3; Copper: 8.86 g/ cm3; Bronze: 9.87 g/ cm3, identify the metal. Show your work. (1 mL = 1 cm3)

5. When a sample of a metal alloy that has a mass f 9.00 g is placed into a graduated cylinder containing water, the volume reading in the cylinder increases from 16.0 mL to 19.5 mL. What is the density of the alloy sample in grams per mL?

6. In the boxes below (all the same size), the dark circles represent particles of matter (each particle has the same mass). Which box has the greatest density? EXPLAIN.

| |A [pic] | |B [pic] | |C [pic] | |D [pic] |

Percentage Error

Percentage Error is a way for scientists to express how far off a laboratory value is from the commonly accepted value.

The formula is:

% error = │Accepted value – Experimental value│ x 100

Accepted value

The symbol “│x │” means absolute value.

Practice: Determine the percentage error in the following problems.

1. Experimental value = 1.24 g

Accepted value = 1.30 g

2. Experimental value = 1.24 x 10-2 g

Accepted value = 9.98 x 10-3 g

3. Experimental value = 252 mL

Accepted value = 225 mL

4. Experimental value = 22.2 L

Accepted value = 22.4 L

5. Experimental value = 125.2 mg

Accepted value = 124.8 m g

Practice

1. Look at the following data:

|Group 1 |Group 2 |Group 3 |

|13.8 ml |17.8 ml |18.8 ml |

|14.1 ml |19.2 ml |19.2 ml |

|13.9 ml |20.2 ml |19.3 ml |

|14 ml |21.0 ml |18.9 ml |

The accepted value for this volume is 19.0 ml.

a. Calculate an average volume for each group.

Group 1 Group 2 Group 3

b. Which group’s data was the most accurate?

c. Which group’s data was the most precise?

d. Calculate the percent error for each group. Show your work.

2. Density =

3. The density of ethanol is 0.789 g/ml. What is the mass of 150 ml of ethanol?

4. Determine the volume that 35.2 g of oil will occupy if the density is 1.6 g/cm3.

Scientific Method

Scenario: You want to determine if sunlight affects the growth of plants. If so, what amount of light exposure would be optimum for plant growth?

Design:

Think about:

• What variable you are changing and which variables must remain constant from group to group.

• How many groups to set up

• What is the data that you will record.

• Set up a group to use as a standard for comparison (the control group).

Variable I will control to be DIFFERENT from group to group: ________________________________

Constants:___________________________________________________

___________________________________________________________

What data are you recording?___________________________________

Control:_____________________________________________________

Terms:

Independent Variable: _______________________________________________

Dependent Variable: ________________________________________________

Control: __________________________________________________________

Constants: ________________________________________________________

Conclusion: ________________________________________________________

Practice: Read the following scenarios.

I. A chemistry class wants to find out how size of reactant particles affects the rate (speed) of a chemical reaction. They ran a controlled experiment with the following data:

|Reactant Particle Size |Reaction Time (s) |

|(all put into 40ml of water) | |

|1 full tablet |109 |

|½ size pieces (2 total pieces) |88 |

|¼ size pieces (4 total pieces) |64 |

|1/8 size pieces (8 total pieces) |49 |

Independent Variable: _______________________________________________

Dependent Variable: ________________________________________________

Control Group: _____________________________________________________

Constants (controlled variables): _______________________________________

Conclusion: ________________________________________________________

II. A chemistry class wants to find out how temperature affects the rate (speed) of a chemical reaction. They ran a controlled experiment with the following data:

|Temperature |Reaction Time (s) |

|(all put into 40ml of water) | |

|25°C (room temp) |113 |

| 50°C |88 |

|70°C |57 |

|90°C |28 |

Independent Variable: _______________________________________________

Dependent Variable: ________________________________________________

Control Group: _____________________________________________________

Constants (controlled variables): _______________________________________

Conclusion: ________________________________________________________

Scientific Notation

Scientific notation expresses numbers as a multiple of 2 numbers

(ex. 6 x 1023 = 1 mol)

The 1st number (X) The 2nd number

1 ≤ X < 10 is 10 raised to a power

Circle the numbers that are written in scientific notation:

a. 3.7 x 10 1 c. 121 x 10 8 e. 67 x 104

b. 133 d. 7.627 x 10 -5

Practice: Write in scientific notation:

a. 3755

b. 6,000,000,000

c. 0.00087

d. 40

Convert the following to scientific notation:

1) 45,700 ____________________________________

2) 0.009______________________________________

3) 23_________________________________________

4) 0.9________________________________________

5) 24,212,000__________________________________

6) 0.000665____________________________________

Convert the following to scientific notation:

17) 21.9______________________________________

18) 0.00332___________________________________

19) 321______________________________________

20) 0.1_______________________________________

21) 1492______________________________________

22) 0.2713_____________________________________

23) 314159____________________________________

24) 6022______________________________________

25) 0.12011____________________________________

Convert the following numbers in scientific notation to expanded form:

26) 3.825 x 103 ________________________________

27) 6.3 x 104 __________________________________

28) 2.3 x 10-2 __________________________________

29) 4.44 x 10-6 _________________________________

30) 7.121 x 109 ________________________________

31) 1.2 x 10-1 __________________________________

32) 1.8 x 102 ___________________________________

33) 8.1 x 10-4 __________________________________

34) 6.7 x 105 ___________________________________

35) 3.4 x 107___________________________________

Metric Conversions Review: Make the following metric conversions

Metrics, Density and Percent Error

1. Make the following metric conversions. You may need to use the chart in your packet for some of the conversions.

a. 750 mg to g ___________________ c. 45 dm to km _________________________

b. 0.052 csec to msec _____________ d. 6700 g to kg_________________________

c. 0.00045 mm to µm ______________ e. 225 ng to g __________________________

2. Finding Percent (%) Error: % Error = │lab value – actual value│ x 100

actual value

a. A student does a lab to determine the molar mass of baking soda. The actual molar

Mass is 84 g/mol. His lab results show that the molar mass is 91 g/mol. Find his percent error.

b. A student does a lab to determine the density of aluminum. He first masses the aluminum rods, then reads the water level on the graduated cylinder, immerses the aluminum and re-reads the graduated cylinder. His data are given below.

i. Complete the table. Include units!

|Mass of Rod |Initial Water Level |Final Water Level |Volume of Aluminum Rod |Density |

|25.50 g |50.2 mL |61.3 mL | | |

|15.50 g |50.4 mL |57.0 mL | | |

|10.05 g |50.5 mL |55.1 mL | | |

Average Density : ___________

ii. The actual density of aluminum is 2.7 g/cm3. Find the percent error using the average density.

iii. How was the student’s accuracy? How was his precision? EXPLAIN!

3. The density of Iron is 7.8 g/cm3. Use this information to answer the questions below:

a. Find the mass of 70.0 cm3 of iron. ____________________________

b. Find the volume of 23 g of iron. ____________________________

c. The length of an iron rod is 3.5 cm, the width of the rod is 2.0 cm and the thickness of the rod is 1.0 cm. Find the volume and the mass of the rod.

Volume = __________ Mass = _____________

4. The density of nitrogen, the gas that makes up 80 % of our air, is 1.25 g/L. Use this information to answer the problems below:

a. Find the volume of 35 kg of nitrogen. (HINT: First change kg to g).

b. Find the mass of 500 L of nitrogen.

c. Why do you think the density of nitrogen is given in g/L instead of g/cm3?

5. Change the following measurements from standard to scientific notation.

a. 0.00230 ________________ b. 5,467_______________________

6. Change the following measurements from scientific to standard notation.

a. 3.41 x 10-3 _________________ b. 7.6 x 105 ____________________

MEASUREMENT REVIEW #1

1. Write down one qualitative measurement and one qualitative measurement.

_____________________ ______________________

2. Fill in the chart below:

|Quantity |Definition |Unit |Equipment |

| |Duration | | |

| | |Liters | |

|Length | | | |

| | | |Triple-beam Balance |

| |Amount of heat energy | | |

3. Draw a bull’s eye that illustrates trails that would be precise but not accurate.

4. Reading lab equipment

[pic] [pic]

Measurement: __________________ _____________________

5. Make the following metric conversions:

K H D __(unit)__ d c m

a. 150mg = ______________ g k. 28km = ___________________ cm

b. 5.0m = ________________ km f. 125mg = ___________________cg

6. Dimensional Analysis:

Real Conversion factors:

2.54cm = 1 inch 1 mile = 5280 feet

3.79 L = 1 gallon 454g = 1 pound

16 ounces = 1 pound 1 calorie = 4.18 Joules

1 mL = 1 cm3 1 mole = 6.02 X 1023 atoms

Convert the following:

a. 12.5 inches = _____________ cm d. 8.5 pounds = ________________ ounces

b. 435 grams = ______________ pounds e. 72 liters = ______________ gallons

c. 2.5 pounds = ______________ grams f. 4 moles = ________________ atoms

7. Solve the following problems related to density:

a. If the mass of an object is 75.0 grams and it has a density of 2.5 g/cm3, what is its volume?

b. If an object has a volume of 125 ml and a density of 1.15 g/ml, what is its mass?

8. Define the following terms:

Independent Variable -

Dependent Variable -

Control -

Constant -

CP Chemistry

Unit 1B: Measurement Review #2

1. When solving a problem:

a. The factor being tested is called the _________________________

b. A possible answer to the problem made before the experiment is a ________________

c. The comparison group in the experiment is called the _______________________

2. An idea that explains how nature behaves, but not why is a _____________________. An idea on why nature behaves the way it does is called a _________________________.

3. What is the SI base unit for:

mass _______________________ amount of substance __________________

temperature _________________ length ______________________________

time _______________________

4. What is a derived unit? Give examples. ___________________________________________

____________________________________________________________________________________________________________________________________________________________

5. What is the difference between mass and weight? ___________________________________

____________________________________________________________________________________________________________________________________________________________

6. When making a measurement, how many estimated digits are there? ____________________

Where is this digit? _____________________________________________________________

7. What is dimensional analysis? __________________________________________________

______________________________________________________________________________

8. Given the following data, tell whether the data is precise, accurate, both, or neither:

a. 15.06 g; 15.09 g; 15.10 g (actual measurement=18.25g) _______________________

b. 5.70 g; 8.63 g; 4.9 g (actual measurement=6.25g) ____________________________

c. 45 mL; 44.8 mL; 45.1 mL (actual measurement=45.0mL) _____________________

9. Convert the following:

a. 65.20 cm = _____________ m d. 125.8 dg = _______________kg

b. 0.0573 Mm = ___________ mm e. 64.9 nL = ________________(L

c. 49.68 pg = _____________ g f. 8.2 nm = _________________km

10. Place the following into scientific notation:

a. 123,000 _________________ c. 0.00350 _________________________

b. 30. _____________________ d. 0.50 ____________________________

11. Write these numbers in ordinary notation:

a. 7.51 X 103 __________________ b. 2.30 X 10-3 _______________________

12. A student gets a density of 2.24 g/cm3 for sulfur. The actual density is 2.08 g/cm3. Determine the percent error.

13. Use dimensional analysis to solve the following:

a. 8.92 days = ____________________ seconds

b. 1469 cm = ____________________ feet ( 1 inch = 2.54 cm)

14. Find the density of an object with a mass of 18.90 g and a volume of 17 cm3.

15. Find the mass of an object with a volume of 23.9 cm3 and a density of 3.972 g/cm3.

16. Find the volume of an object with a mass of 16.00 g and a density of .872 g/cm3.

-----------------------

- A combination of base units

- Independent of other units

- 1 single measurement

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#4

#2

#3

#1

Accuracy:

Precision:

A

B

C

A

B

C

Precision with regard to equipment depends on the amount of _____________.

Rule: You must estimate one digit beyond the calibration.

#3: Calibrated to the ______________

Must estimate one digit so record to the ______________

#2: Calibrated to the ______________

Must estimate one digit so record to the ________________

#1: Calibrated to the ______________

Must estimate one digit so record to the ______________

40 cm 50 cm

40 cm 41 cm

5 g 508mg

1,500 mL 1.5 L

63 cm 6 m

536 cm 53.6dm

3.6 m 36 cm

43 mg 5 g

●THINGS TO MEMORIZE●

1. SI units (book)

2. 1 cm3 (solids) = 1 mL(liquids)

3. 1dm3 = 1 L

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