NOTES: MEASUREMENT AND SIGNIFICANT DIGITS



Unit 1B NOTES: MEASUREMENT of MATTER

lab equipment –

1.

2.

3.

Types of Measurements/Data =

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

|Quantity |Definition (match from list below) |Typical Unit | SI Unit |Base unit (B) / |Equipment |

| | | | |Derived unit | |

| | | | |(D) | |

|Mass | | | | | |

| | | | | | |

|Volume | | | | | |

| | | | | | |

|Density | | | | | |

| | | | | | |

|Length | | | | | |

| | | | | | |

|Time | | | | | |

| | | | | | |

|Temperature | | | | | |

| | | | | | |

Definitions:

A) a straight line distance between 2 points

B) the quantity of matter in an object

C) the ratio (fraction) of mass to volume

(mass / volume)

D) the amount of space an object takes up

E) the measure of the average kinetic energy of a substance/ a measure of how fast the particles of a substance is moving (vibration of molecules)

F) used to compare the durations of events and the intervals between them.

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)



Temperature – average ______________energy

Celsius temperature scale: At _____°C water freezes. At ________°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 _______________________________________.

Practice Convert the following

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

c. 273 ºC to Kelvin f. zero K to Celsius

2. 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.

3. 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.

Dimensional Analysis dimensional analysis –



and

more than one to convert -



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.

|[pic] |[pic] |

• 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: How many hours are in 5.00 days?

5.00 days 24 hours = 120. Hour

1 day

As the year progresses, you will be doing problems that use this technique so DO NOT ASK IF YOU CAN DO THIS A SIMPLER WAY. IT IS BEING TAUGHT IN THIS CHAPTER SO THAT YOU BETTER UNDERSTAND THE FUTURE HARDER UNITS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Example of a future chapter:

[pic]

For now, let’s stay simple:

Example: How many days is 655 hours?

You Try: How many inches is 9.35 feet? (1 foot = 12 inches)

CONVERSIONS USING DIMENSIONAL ANALYSIS:

UNIT Conversion factors:

3.79 L = 1 gallon 1 mole = 6.02 X 1023 atoms

16 cups = 1 gallon 2.54cm = 1 inch

16 ounces = 1 pound 1 foot = 12 inches

454g = 1 pound 1 mile = 5280 feet

1 gallon = 4 quarts 237 mL = 1 cup

1 calorie = 4.18 Joules 1 mL = 1 cm3

1 food calories = 1,000 calories

a. 5.7 inches = _____________ cm

Conversion factor: Set up & solve:

b. 85 ounces = ________________ pounds

Conversion factor: Set up & solve:

c. 125 grams = ______________ pounds

Conversion factor: Set up & solve:

d. 72 cm3 = ______________ mL

e. 2.5 moles = ______________ atoms

f. 24 Joules = ____________ calories

g. 6 gallons = _________________ liters

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 = ________________ L (one step)

Metric Unit Abbreviations - preview

Use the word bank to 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 _______

mnemonic:

|prefix |Kilo (k) |Hecto (h) |

Density = Mass /Volume or D = m/V

Density:

Sample: solved density problems:

a. Determine the density of an object with a mass of 13.25 g and occupies of volume of 3.7 cm3.

[pic] = 3.6g/cm3

b. Gold has a density of 19.30 g/cm3. What is the mass of a piece of gold that has a volume of 5.35 cm3?

[pic] = [pic] x = 103g or

c. What is the volume of a piece of aluminum with a density of 2.70 g/cm3 and a mass of 415 g?

[pic] = [pic] x = 154cm3 or

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 = │Experimental value - Accepted 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

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

TRY READING EQUIPMENTS

| |Calibration lines are in the one’s spot |*Place Value to Estimate |

| | |And record to the tenth’s spot |

|[pic] |Ones spot |Tenth spot |

| | | |

| | |36.5ml |

| |It is between 36 and 37ml | |

| | |(its more than 36 but less than 37 and I must |

| | |estimate to the tenth spot. |

Smallest calibration lines: ___tenth__________

Place Value to Estimate(Final answer) : __hundredths___

SIGNIFICANT DIGITS: Determining Accuracy of Lab Equipment by Evaluating Measurements

All digits that are read or estimated in lab are considered “significant digits”. Any measurement given in a lab report communicates three things to the reader: the numeric value of the measurement, the degree of calibration of the equipment and the unit the measurement was taken in.

Here are some examples of determining significant digits from lab measurements:

|Measurement |Equipment Calibrated to: |Read To: |# of significant digits |

| | |(includes estimate) | |

|14.0g |ones place |tenths place |3 |

|25mL |tens place |ones place |2 |

|0.035mL |hundredths place |thousandths place |2** |

** notice that “place holder” zeros (in front) are not actually measured, so are not considered significant digits!

PRACTICE:

1. Each diagram below represents a piece of lab equipment used to measure liquid volume. Use the student’s measurement to fill in the calibration boxes.

[pic]

[pic]

[pic]

Scientific notation expresses numbers as a multiple of 2 numbers

The numbers are written in scientific notation:

a. 3.7 x 10 1 (one number than the dot!)

b. 7.627 x 10 -5 (one number than the dot!)

The numbers are NOT written in scientific notation:

c. 93.7 x 10 1 (two numbers than the dot – NOT CORRECT!)

d. 0.627 x 10 -5 (THERE IS NOT EVEN A NUMBER BEFORE THE dot – NOT CORRECT!)

Write in scientific notation:

a. 3755 _________________________

b. 6,000,000,000 _________________________

c. 0.00087 _________________________

d. 40 _________________________

Metrics, Density and Percent Error

1. Make the following metric conversions.

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

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

e. 0.00045 mm to µm ______________ f. 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.

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?

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.

Dimensional Analysis Practice #1

Use dimensional analysis to convert the units below. You must show your set up and cancellation to get credit. Use the conversion factors found in your notes to.

ONE STEP PROBLEMS:

a. 795g to pounds _______________

b. 525mL to cups ________________

c. 99 quarters to dollars _______________

d. 0.0050m to mm _______________

e. 2.75kJ to J _______________

TWO STEP PROBLEMS

a. 25 gallons to mL (16 cups = 1 gallon) ________________

b. 2.4 dm to feet _______________

THREE STEP PROBLEM

a. 2.4miles to cm ________________

Dimensional Analysis Practice #2

Use dimensional analysis to convert the units below. You must show your set up and cancellation to get credit. Use the conversion factors found in your notes to.

a. A school day is approximately 6.5 hours long. How many minutes is this?

b. There are 355mL of diet pepsi in a can. How many cups is this?

c. My car has a 20 gallon tank. How many liters of gasoline will it hold?

d. Find the weight, in pounds, of 1500g of flour.

e. Convert 50,000 feet to miles.

f. A student with a learner’s permit must have a minimum of six months of supervised practice driving before obtaining a provisional license. How many hours of driving is this? (assume that 1 month = 30 days).

g. A new born baby weighs 3180g. How many ounces does he weigh?

h. How many miles does a student run in a “500 yard dash”?

i. Currently 1 US dollar is equal to 0.68 euros. How many quarters would be equal to 500 euros?

Dimensional Analysis Practice #3

Use dimensional analysis to convert the units below. You must show your set up and cancellation to get credit. Use the conversion factors found in your notes to.

ONE STEP PROBLEMS:

a. 225 sec to csec _______________

d. 24pounds to g ________________

TWO STEP PROBLEMS

c. 65kJ to calories ________________

d. 530 mm to km _______________

THREE STEP PROBLEM

e. 54 gallons to tablespoons (1T = 15mL) ________________

f. 20 km to inches ________________

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

Base Units

Derived Units

- A combination of base units

- Example: volume (l)x(w)x(h) and density (m/V)

- Independent of other units

- 1 single measurement

- example: mass, time

K = ºC + 273 ºC = K – 273

2ft

1 ft

12 in

24 in

1 ft

12 in

24 in

in

24 in

Will be provided during Chapter 3 test!

m

g

L

dam dag daL

LEFT IS LARGER

LARGER GETS “1”

1.

Fill in the table from the videos

2.

km kg kL

hm hg hL

dm dg dL

cm cg cL

mm mg mL

ml cm km mg g dag

lt m l mm dg kg

Left is larger. Larger gets the “1”

Ï%HELPFUL TO MEMORIZEÏ%

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

2. 1dm3 = 1 L

●HELPFUL TO MEMORIZE●

1 cm3 (solids) = 1 mL(liquids)

1dm3 = 1 L

g, kg

g/ml, g/cm3, kg/L

ml, cm3, L

19.30g = 1 cm3 for gold

5.35cm3 x 19.30g = 103g

1 cm3

2.70g = 1 cm3 for aluminum

415g x 1 cm3 = 154cm3

2.70g

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 ______________

Hundreds tens ones . tenth hundredth thousandth

← Record (one to the Right)

( equipment calibration

[pic]

Record the mass on the balance above ____________

Hundreds tens ones . tenth hundredth thousandth

← Record (one to the Right)

( equipment calibration

Student’s measurement = 8.7 mL

Calibration lines:__ones___

Recorded to: __tenth_______

# of significant digits: ___2____

Student’s measurement = 787 mL

Calibration lines:______

Recorded to: __ones_______

# of significant digits: ___3____

Student’s measurement = 270.0 mL

Calibration lines:______

Recorded to: __tenth_______

# of significant digits: ___4____

The 2nd number

is 10 raised to a power

The 1st number

1 ≤ X < 10

If the original number is 1 than the exponent will be positive

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