Unit 2 Notes Packet NOTES 5
SIGNIFICANT FIGURES
*Measurements in science may be considered to have:
a. accuracy– how close a measurement comes to the actual or true value
b. precision–how reproducible the measurements are (ie. how close the trial values are to each other)
*SIGNIFICANT FIGURES
Measurements are reported in significant figures.
Significant figures include all digits that can be read precisely, plus a last digit that must be estimated.
*To determine significant figures (“sig figs”) in a value, the following rules are used:
1. All non-zero numerals are significant
2. If a zero is trapped, it is significant.
A zero may be trapped by: a) an ending decimal
b) another sig fig
3. Leading zeros (at the beginning of the number) are never significant.
4. Ending zeros are only significant if there is a decimal showing.
EXAMPLES: Rounded to 3 sig figs Rounded to 1 sig fig
1.020 4 sig figs _____1.02______1______
45.0 ____3____ sig figs _____45.0______50______
0.00003 ____1____ sig figs ___0.0000300______0.00003______
154 ____3____ sig figs ______154______200______
_
54,000,000 ____2____ sig figs ___54,000,000______50,000,000_____
_
97,000,000. ____8_____ sig figs ___97,000,000______100,000,000___
NOTES 6
SCIENTIFIC NOTATION
A method of writing numerical values in science, especially those that are very large or very small, is known as
scientific notation (or exponential notation).
It always consists of a number with only one non-zero digit to the left of the decimal, followed by a power of ten (ie. 2.5 x 107 or 3.62 x 10-4).
Standard Notation Scientific Notation
45,000,000 ______4.5 x 107______
325 ______3.25 x 102______
0.000150 ______1.50 x 10-4______
0.00000000268 ______2.68 x 109______
_
_____970,000______9.70 x 105
_____0.006330______6.330 x 10-3
*When performing calculations involving multiplication and/or division, the number of sig figs in the final answer must be the same as the lowest number of sig figs in the given values.
EXAMPLES: 4.245 x 104 (2.200 x 103) X (7.10 x 10-7)
2.9 x 10-3
Find the “EE” (“2nd, comma” on graphing calculators) or “EXP” or “x10n” button on your calculator and plug in the following:
(4.245 EE 4) divided by (2.9 EE -3) (2.200 EE 3) times (7.10 EE -7)
= 1.5 x 107 = 1.56 x 10-3
NOTES 7
USING METRIC UNITS
SI Units (International System of Units)
There are seven SI base units from which all other units can be derived:
Quantity Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Temperature Kelvin K
Amount of substance mole mol
Electric current ampere A
Luminous intensity candela cd
All other units are SI derived units (ie. volume, density)
*COMMON MEASUREMENT UNITS IN CHEMISTRY
Length – the distance between two points
(measured in meters – commonly centimeters or millimeters)
Mass – the amount of matter contained in an object
(measured in grams)
Volume – the amount of space an object occupies
(measured in liters – commonly milliliters)
Temperature – a measure of the average kinetic energy contained in a material
(measure in Kelvins or degrees Celsius)
METRIC PREFIX LIST
PREFIX SYMBOL NUMERICAL VALUE EXPONENT
yotta Y 1,000,000,000,000,000,000,000,000 1024
zetta Z 1,000,000,000,000,000,000,000 1021
exa E 1,000,000,000,000,000,000 1018
peta P 1,000,000,000,000,000 1015
tera T 1,000,000,000,000 1012
giga G 1,000,000,000 109
mega M 1,000,000 106
kilo k 1,000 103
NO PREFIX 1 100
centi c 0.01 10-2
milli m 0.001 10-3
micro µ 0.000001 10-6
nano n 0.000000001 10-9
pico p 0.000000000001 10-12
femto f 0.000000000000001 10-15
atto a 0.000000000000000001 10-18
zepto z 0.000000000000000000001 10-21
yocto y 0.000000000000000000000001 10-24
*METRIC CONVERSIONS
Metric Prefixes to Know:
mega “M” _____106______
kilo “k” _____103______
centi “c” _____10-2______
milli “m” _____10-3______
micro “m” _____10-6______
nano “n” _____10-9______
pico “p” _____10-12______
“King Henry Doesn’t Usually Drink Chocolate Milk”
Example #1
1dg = ? kg
To go from deci to kilo you move the decimal 4 places to the left
Therefore, 1dg = 0.0001 kg
Example #2
10hL = ? mL
To go from hecto to milli you move the decimal 5 places to the right
Therefore, 10 hL =1,000,000 mL
EXAMPLES:
150 centimeters = ___0.0015______kilometers
0.025 gigawatts = ___25,000______kilowatts
10 milligrams = ___10,000______micrograms
125,000 nanoliters = ___0.000125______liters
EXAMPLES:
7.30 x 104 mg = __7.30 x 101______g
2.0 x 101 MHz = __2.0 x 107 ______Hz
1.35 x 10-7 m = __1.35 x 102______nm
NOTES 8
DENSITY
Density – the amount of matter in an object per unit volume
*More dense materials will sink in less dense ones
*As the temperature of a material increases, the density tends to decrease
*Cutting an object into smaller pieces does not change its density
Question: Would the density of an object be the same on the earth and the moon?
Density = mass m = mass (in grams)
volume V = volume (in cm3 or mL)
D = density (in g/cm3 or g/mL)
Note: *1 mL = 1 cm3 = 1 cc
EXAMPLES: http://www.youtube.com/watch?v=-CDkJuo_LYs
A student finds a shiny piece of metal she thinks is aluminum. In the lab, she determines that the metal has a volume of 245 cm3 and a mass of 612 g. Is the metal aluminum? (Density of aluminum = 2.70 g/cm3)
D= mV D= 612 g245 cm3 D=2.49796 = 2.50 gcm3
Compare the density of the piece of metal (2.50 g/cm3) to that of aluminum (2.70 g/cm3) – the object is not aluminum
A piece of iron has a mass of 2.25 kg. What is its volume? Look up the density of iron: 7.87 g/cm3
D= mV V= mD V= 2,250 g7.87 gcm3 V=285.9 = 286 cm3
A lead sinker has a volume of 5.0 mL. What is its mass? Look up the density of lead: 11.34 g/cm3
D= mV m=D x V m=11.35gmL x 5.0 mL m=56.75 = 57 g
NOTES 9
DIMENSIONAL ANALYSIS: Single Step
In order to convert between systems, it is necessary to use “dimensional analysis” (a method of canceling units on number values in calculations).
Dimensional analysis uses “conversion factors” (ratios representing equivalent values of two different units).
EXAMPLES OF CONVERSION FACTORS:
12 inches = 1 foot 12 inches __1 foot__
1 foot 12 inches
1000 mL = 1 Liter 1000 mL __1 Liter__
1 Liter 1000 mL
inches to meters 39.37 inches __1 meter__
1 meter 39.37 inches
quarts to liters __1 quart__ _0.946 liters_
0.946 liters 1 quart
3.26 g/cm3 3.26 g _1 cm3_
1 cm3 3.26 g
EXAMPLES OF DIMENSIONAL ANALYSIS PROBLEMS:
*How many feet are in 1.29 miles?
1.29 miles1 5280 feet1 mile = 6811.2 = 6810 feet
*How many meters are in 2.5400 inches?
2.5400 inches1 1 meter39.37 inches= 0.0645161 = 0.06452 meters
NOTES 10
DIMENSIONAL ANALYSIS: Multi-Step
EXAMPLES OF DIMENSIONAL ANALYSIS PROBLEMS:
How many ounces are in 0.0250 kg of salt?
0.0250 kg1 1000 g1 kg 1 ounce28.350 g= 0.88183 = 0.882 ounces
How many furlongs are in 5.00 x 103 mil?
5.00 x 103 mil1 0.001 inches1 mil 1 foot12 inches 1 furlong660 feet= 0.00063131 = 0.000631 furlongs