Ch. 5 Notes---Measurements & Calculations Qualitative vs. Quantitative Qualitative measurements...

Ch. 5 Notes---Measurements & Calculations Qualitative vs. Quantitative

• Qualitative measurements give results in a descriptive nonnumeric form. (The result of a measurement is an _____________ describing the object.)

*Examples: ___________, ___________, long, __________...

• Quantitative measurements give results in numeric form. (The results of a measurement contain a _____________.)

*Examples: 4’6”, __________, 22 meters, __________...

Accuracy vs. Precision

• Accuracy is how close a ___________ measurement is to the ________ __________ of whatever is being measured.

• Precision is how close ___________ measurements are to _________ ___________.

adjective

short heavy cold

number

600 lbs. 5 ºC

singlevaluetrue

severalothereach

Click Below for Lecture Links

• http://danreid.wikispaces.com/file/view/Ch.%203%20Notes%20%28Scientific%20Measurements%29%20Part%201.swf

• http://danreid.wikispaces.com/file/view/Ch.%203%20Notes%20%28Scientific%20Measurements%29%20Part%202.swf

Practice Problem: Describe the shots for the targets.

Bad Accuracy & Bad Precision Good Accuracy & Bad Precision

Bad Accuracy & Good Precision Good Accuracy & Good Precision

Significant Figures

• Significant figures are used to determine the ______________ of a measurement. (It is a way of indicating how __________ a measurement is.)

*Example: A scale may read a person’s weight as 135 lbs. Another scale may read the person’s weight as 135.13 lbs. The ___________ scale is more precise. It also has ______ significant figures in the measurement.

• Whenever you are measuring a value, (such as the length of an object with a ruler), it must be recorded with the correct number of sig. figs.

• Record ______ the numbers of the measurement known for sure.

• Record one last digit for the measurement that is estimated. (This means that you will be ________________________________ __________ of the device and _____________ what the next number is.)

more

marksreading in between the

precise

ALL

second

precision

estimating

Significant Figures

• Practice Problems: What is the length recorded to the correct number of significant figures?

(cm) 10 20 30 40 50 60 70 80 90 100

length = ________cm

length = ________cm11.65

58

Rules for Counting Significant Figures in a Measurement

• When you are given a measurement, you will need to be aware of how many sig. figs. the value contains. (You’ll see why later on in this chapter.)

Here is how you count the number of sig. figs. in a given measurement:

#1 (Non-Zero Rule): All digits 1-9 are significant.

*Examples: 2.35 g =_____S.F. 2200 g = _____ S.F.

#2 (Straddle Rule): Zeros between two sig. figs. are significant.

*Examples: 205 m =_____S.F. 80.04 m =_____S.F.

7070700 cm =_____S.F.

#3 (Righty-Righty Rule): Zeros to the right of a decimal point AND anywhere to the right of a sig. fig. are significant.

*Examples: 2.30 sec. =_____S.F. 20.0 sec. =_____S.F.

0.003060 km =_____S.F.

3 2

3 4

5

3 3

4

Rules for Counting Significant Figures in a Measurement

#4 (Bar Rule): Any zeros that have a bar placed over them are sig. (This will only be used for zeros that are not already significant because of Rules 2 & 3.)

*Examples: 3,000,000 m/s =_____S.F. 20 lbs =____S.F.

#5 (Counting Rule or Exact #’s): Any time the measurement is determined by simply counting the number of objects, the value has an infinite number of sig. figs. (This also includes any conversion factor known exactly without it being rounded off for ease of use!)

*Examples: 15 students =_____S.F. 29 pencils = ____S.F.

7 days/week =____S.F. 60 sec/min =____S.F.

1 inch = exactly 2.54 cm...The measurement “2.54 cm” has ____ S.F.

4 2

∞

∞

∞

∞

∞

Scientific Notation• Scientific notation is a way of representing really large or small

numbers using powers of 10.

*Examples: 5,203,000,000,000 miles = 5.203 x 1012 miles

0.000 000 042 mm = 4.2 x 10−8 mm

Steps for Writing Numbers in Scientific Notation

(1) Write down all the sig. figs.

(2) Put the decimal point between the first and second digit.

(3) Write “x 10”

(4) Count how many places the decimal point has moved from its original location. This will be the exponent...either + or −.

(5) If the original # was greater than 1, the exponent is (__), and if the original # was less than 1, the exponent is (__)....(In other words, large numbers have (__) exponents, and small numbers have (_) exponents.

+

+−

−

477,000,000 miles = _______________miles

0.000 910 m = _________________ m

6.30 x 109 miles = ___________________ miles

3.88 x 10−6 kg = __________________ kg

Scientific Notation

• Practice Problems: Write the following measurements in scientific notation or back to their expanded form.

4.77 x 108

9.10 x 10−4

6,300,000,000

0.00000388

−

Calculations Using Sig. Figs.

• When adding or subtracting measurements, all answers are to be rounded off to the least # of ___________ __________ found in the original measurements.

• When multiplying or dividing measurements, all answers are to be rounded off to the least # of _________ _________ found in the original measurements.

Practice Problems:

2.83 cm + 4.009 cm − 2.1 cm = 4.739 cm ≈_____ cm

36.4 m x 2.7 m = 98.28 m2 ≈ _____ m2

0.52 g ÷ 0.00888 mL = 5.855855 g/mL ≈ ____ g/mL

+

≈ 157.17 (only keep 2 decimal places)

Example:

decimal places

significant figures

4.7

98

5.9

(only keep 1 decimal place)

(only keep 2 sig. figs)

(only keep 2 sig. figs)

The SI System (The Metric System)

• Here is a list of common units of measure used in science:

Standard Metric Unit Quantity Measured

kilogram, (gram) ______________

meter ______________

cubic meter, (liter) ______________

seconds ______________

Kelvin, (˚Celsius) ______________

• The following are common approximations used to convert from our English system of units to the metric system:

1 m ≈ _________ 1 kg ≈ _______ 1 L ≈ 1.06 quarts

1.609 km ≈ 1 mile 1 gram ≈ _______________________

1mL ≈ _____________ volume 1mm ≈ thickness of a ________

mass

length

volumetime

temperature

1 yard

sugar cube’s

2.2 lbs.

mass of a small paper clip

dime

The SI System (The Metric System)

Metric Conversions• The metric system prefixes are based on factors of _______. Here is a

list of the common prefixes used in chemistry:

kilo- hecto- deka- deci- centi- milli-

• The box in the middle represents the standard unit of measure such as grams, liters, or meters.

• Moving from one prefix to another involves a factor of 10.

*Example: 1000 millimeters = 100 ______= 10 ______ = 1 ______

• The prefixes are abbreviated as follows:

k h da g, L, m d c m

*Examples of measurements: 5 km 2 dL 27 dag 3 m 45 mm

grams Liters meters

10

cm dm m

Metric Conversions

• To convert from one prefix to another, simply count how many places you move on the scale above, and that is the same # of places the decimal point will move in the same direction.

Practice Problems:

380 km = ______________m 1.45 mm = _________m

461 mL = ____________dL 0.4 cg = ____________ dag

0.26 g =_____________ mg 230,000 m = _______km

Other Metric Equivalents

1 mL = 1 cm3 1 L = 1 dm3

For water only:

1 L = 1 dm3 = 1 kg of water or 1 mL = 1 cm3 = 1 g of water

Practice Problems:

(1) How many liters of water are there in 300 cm3 ? ___________

(2) How many kg of water are there in 500 dL? _____________

380,000

4.61

260

0.00145

0.0004

230

0.3 L

50 kg

kilo- hecto- deka- deci- centi- milli-

Metric Volume: Cubic Meter (m3)

10 cm x 10 cm x 10 cm = Liter

grams Liters meters

Area and Volume Conversions

• If you see an exponent in the unit, that means when converting you will move the decimal point that many times more on the metric conversion scale.

*Examples: cm2 to m2 ......move ___________ as many places

m3 to km3 ......move _____ times as many places

Practice Problems: 380 km2 = _________________m2

4.61 mm3 = _______________cm3

k h da g, L, m d c m

twice

3

380,000,000

0.00461

Additional Metric Prefixes

Notice that the jump from one prefix to another is a factor of 1000, or 3 decimal places!

Mass vs. Weight• Mass depends on the amount of

___________ in the object.

• Weight depends on the force of ____________ acting on the object.

• ______________ may change as you move from one location to another; ____________ will not.

• You have the same ____________ on the moon as on the earth, but you ___________ less since there is less _________ on the moon.

matter

gravity

Weight

mass

mass

gravityweigh

Mass = 80 kg

Weight = 176 lbs.

Mass = 80 kg

Weight = 29 lbs.

Density

• Density is a ___________ of an object’s mass and its volume.

• Density does not depend on the _________ of the sample you have.

• The density of an object will determine if it will float or sink in another phase. If an object floats, it is _______ dense than the other substance. If it sinks, it is ________ dense.

• The density of water is 1.0 g/mL, and air has a density of 0.00129 g/mL (or 1.29 g/L).

• Density = Mass/Volume

m

D V X

Mass = D x V

ratio

size

lessmore

Density = m/V

Volume = m/D

DensityPractice Problems:

(1) The density of gold is 19.3 g/cm3. How much would the mass of a bar of gold be? Assume a bar of gold has the following dimensions: L= 27 cm W= 9.0 cm H= 5.5 cm

(2) Which picture shows the block’s position when placed in salt water?

(3) Will the following object float in water? _______

Object’s mass = 27 g

Object’s volume= 25 mL

Volume = L x W x HVolume = 27 x 9.0 x 5.5 = 1336.5 cm3

mass = D x Vmass = 19.3 g/cm3 x 1336.5 cm3 = 25,794.45 g

mass ≈ 26,000 g = 26 kg ≈ 57 lbs.

No! It will sink. (D > 1)

Measuring Temperature

• Temperature is the ____________ or ____________ of an object.

• The Celsius temperature scale is based on the freezing point and boiling point of __________.

F.P.= 0˚C B.P.= 100˚C

• The Kelvin temperature scale, sometimes called the “absolute temp. scale”, is based on the ____________ temperature possible, absolute zero. (All molecular motion would __________.)

Absolute Zero = 0 Kelvin = −273˚ C

• To convert from one temp. scale to another:

˚C = Kelvin − 273

K= Celsius + 273

Practice Problems: Convert the following

25˚C = _______ K

473 K = _______˚C

hotness coldness

water

loweststop

298

200

(25 + 273)

(473 – 273)

Temperature Scales

Liquid Nitrogen

Evaluating the Accuracy of a Measurement

• The “Percent Error ” of a measurement is a way of representing the accuracy of the value. (Remember what accuracy tells us?)

% Error = (Accepted Value) − (Experimentally Measured Value) x 100 (Accepted Value)

Practice Problem:

A student measures the density of a block of aluminum to be approximately 2.96 g/mL. The value found in our textbook tells us that the density was supposed to be 2.70 g/mL. What is the accuracy of the student’s measurement?

(Absolute Value)

% Error = |2.70−2.96| ÷ 2.70 = 0.096296…x 100 = 9.63% error