Ch. 5 Notes---Scientific Measurement 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

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 taking a __________ at what the next number is.)

more

marksreading in between the

guess

precise

ALL

second

precision

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

For Example

• Lets say you are finding the average mass of beans. You would count how many beans you had and then find the mass of the beans.

• 26 beans have a mass of 44.56 grams.

• 44.56 grams ÷26 =1.713846154 grams

So then what should your written answer be?

How many decimal points did you have in

your measurement?

Rounded answer =

2

1.71 grams

• 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): 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 involving counting.)

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

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

4 2

∞

∞

∞

∞

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)

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.

• 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

volume

timetemperature

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

mass

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 = _________m461 mL = ____________dL 0.4 cg = ____________ dag0.26 g =_____________ mg 230,000 m = _______km

Other Metric Equivalents1 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

Ch. 4 Problem Solving in ChemistryDimensional Analysis

• Used in _______________ problems.

*Example: How many seconds are there in 3 weeks?

• A method of keeping track of the_____________.

Conversion Factor

• A ________ of units that are _________________ to one another.

*Examples: 1 min/ ___ sec (or ___ sec/ 1 min)

___ days/ 1 week (or 1 week/ ___ days)

1000 m/ ___ km (or ___ km/ 1000 m)

• Conversion factors need to be set up so that when multiplied, the unit of the “Given” cancel out and you are left with the “Unknown” unit.

• In other words, the “Unknown” unit will go on _____ and the “Given” unit will go on the ___________ of the ratio.

conversion

units

ratio equivalent

60 607 7

1 1

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How to Use Dimensional Analysis to Solve Conversion Problems

• Step 1: Identify the “________”. This is typically the only number given in the problem. This is your starting point. Write it down! Then write “x _________”. This will be the first conversion factor ratio.

• Step 2: Identify the “____________”. This is what are you trying to figure out.

• Step 3: Identify the ____________ _________. Sometimes you will simply be given them in the problem ahead of time.

• Step 4: By using these conversion factors, begin planning a solution to convert from the given to the unknown.

• Step 5: When your conversion factors are set up, __________ all the numbers on top of your ratios, and ____________ by all the numbers on bottom.

If your units did not ________ ______ correctly, you’ve messed up!

Given

Unknown

conversion factors

multiplydivide

cancel out

Practice Problems: (1)How many hours are there in 3.25 days?

(2) How many yards are there in 504 inches?

(3) How many days are there in 26,748 seconds?

24 hrs1 day

3.25 days

x = 78 hrs

1 ft 12 in.

1 yard 504 in. x x = 14 yards

60 sec1 hr 1 min26,748 sec

x x = 0.30958 days

3 ft

60 minx

24 hrs1 day

Converting Complex Units

• A complex unit is a measurement with a unit in the _____________ and ______________.

*Example: 55 miles/hour 17 meters/sec 18 g/mL

• To convert complex units, simply follow the same procedure as before by converting the units on ______ first. Then convert the units on __________ next.

Practice Problems: (1) The speed of sound is about 330 meters/sec. What is the speed of sound in units of miles/hour? (1609 m = 1 mile)

(2) The density of water is 1.0 g/mL. What is the density of water in units of lbs/gallon? (2.2 lbs = 1 kg) (3.78 L = 1 gal)

1 mile1609 m

3600 sec330m x x = 738 miles/hr1 hr sec

1 kg1000 g

2.2 lbs1.0 g x x 8.3 lbs/gal1 kg mL

1000 mLx =1 L

3.78 L x1 gal

numeratordenominator

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