learning check
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Learning Check. What is the length of the wooden stick? 1) 4.5 cm 2) 4.58 cm 3) 4.584 cm. Measurement and Significant Figures. Every experimental measurement has a degree of uncertainty. The volume, V, at right is certain in the 10 ’ s place, 10mLTRANSCRIPT
Learning CheckLearning Check
What is the length of the wooden stick?
1) 4.5 cm 2) 4.58 cm 3) 4.584 cm
Measurement and Significant Measurement and Significant FiguresFigures
Every experimental measurement has a degree of uncertainty.
The volume, V, at right is certain in the 10’s place, 10mL<V<20mL
The 1’s digit is also certain, 17mL<V<18mL
A best guess is needed for the tenths place. Chapter Two 2
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106,000 aluminum cans, the number 106,000 aluminum cans, the number used in the US every 30 seconds.used in the US every 30 seconds.
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How many cans are used in a year?How many cans are used in a year?
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Scientific NotationScientific Notation# from 1 to 9.999 x 10exponent
800 = 8 x 10 x 10 = 8 x 102
2531 = 2.531 x 10 x 10 x 10
= 2.531 x 103
0.0014 = 1.4 ÷ 10 ÷ 10 ÷ 10
= 1.4 x 10-3
Change to standard form.
1.87 x 10–5 =
3.7 x 108 =
7.88 x 101 =
2.164 x 10–2 =
370,000,000
0.0000187
78.8
0.02164
Change to scientific notation.
12,340 = 0.369 = 0.008 = 1,000. =
1.234 x 104
3.69 x 10–1
8 x 10–3
1.000 x 109
No Cussing!The following 4-Letter
words are forbidden here:
Inch MileFoot PintYard Acre
And we never swear the BIG F (useoC)
Please keep it clean and
Metric
SI SystemSI SystemThe International System of Units
Derived Units Commonly Used in Chemistry
Map of the world where red represents countries which do not use the metric system
The International System of UnitsThe International System of Units
Length meter m
Mass kilogram kg
Time second s
Amount of substance mole mol
Temperature Kelvin K
Electric current amperes amps
Luminous intensity candela cd
Quantity Name Symbol
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16
NEED TO KNOW Prefixes in the SI SystemNEED TO KNOW Prefixes in the SI System
Power of 10 for Prefix Symbol Meaning Scientific Notation_________________________________________________________
mega- M 1,000,000 106
kilo- k 1,000 103
deci- d 0.1 10-1
centi- c 0.01 10-2
milli- m 0.001 10-3
micro- 0.000001 10-6
nano- n 0.000000001 10-9
Significant figuresSignificant figures
Method used to express accuracy and precision.
You can’t report numbers better than the method used to measure them.
67.20 cm = four significant figures
UncertainDigit
Certain Digits
???
Significant figuresSignificant figures
The number of significant digits is independent of the
decimal point.255 31.7 5.60 0.934 0.0150
These numbersAll have three
significant figures!
Rules for Counting Significant figuresRules for Counting Significant figures
Every non-zero digit is Every non-zero digit is ALWAYS significant!ALWAYS significant!
Zeros are what will give Zeros are what will give you a headache!you a headache!
They are used/misused all of the time.
SEE p.24 in your book!
Rules for zerosRules for zerosLeading zeros are notare not significant.
Captive zeros are alwaysare always significant!
0.421 - three significant figuresLeading zeroLeading zero
Trailing zeros areare significant …IFIF there’s a decimal point decimal point in the number!
114.20 - five significant figures
Trailing zeroTrailing zero
???
???
4,008 - four significant figuresCaptive zerosCaptive zeros
???
ExamplesExamples
250 mg
\__ 2 significant figures
120. km
\__ 3 significant figures
0.00230 kg
\__ 3 significant figures
23,600.01 s
\__ 7 significant figures
Significant figures:Significant figures:Rules for zerosRules for zeros
Scientific notationScientific notation - can be used to clearly express significant figures.
A properly written number in scientific notation always has the proper number of significant figures.
0.00321321 = 3.213.21 x 10-3
Three SignificantFigures
Three SignificantFigures
Significant figures and Significant figures and calculationscalculations
An answer can’t have more significant figures than the quantities used to produce it.
ExampleExampleHow fast did you run if youwent 1.0 km in 3.0 minutes?speed = 1.0 km
3.0 min = 0.33 km
min+
-1
/
x
0
2 3
4 5 6
7 8 9
.
CE
EE
log
ln
1/x
x2
cos tan
0.333333
Significant figures and calculationsSignificant figures and calculations
Multiplication and division.Multiplication and division.
Your answer should have the same number of sig figs as the original number with the smallest number of significant figures.
21.4 cm x 3.095768 cm = 66.2 cm2
135 km ÷ 2.0 hr = 68 km/hr
ONLY 3 SIG FIGS!
ONLY 2 SIG FIGS!
Significant figures and calculationsSignificant figures and calculations
Addition and subtractionAddition and subtractionYour answer should have the same number of digits to the right of the decimal point as the number having the fewest to start with.
123.45987 g+ 234.11 g 357.57 g
805.4 g- 721.67912 g 83.7 g
Rounding off numbersRounding off numbers
After calculations, you may need to round off.
If the first insignificant digit is 5 or more, you round up
If the first insignificant digit is 4 or less, you round down.
If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then -
2.57995035 becomes 2.580
34.2004221 becomes 34.20
Examples of rounding offExamples of rounding off
1st insignificant digit1st insignificant digit