Metric System Prefixes
The metric system is a logarithmic system, which means simply that it is based upon powers of ten. Our number system is also based upon powers of ten. Therefore, the metric system allows for the simplest conversion of units.
Conversion requires easily moving the decimal to the right or left.
Metric Prefix Mnemonic Device:
The Good Man King Henry died by drinking chocolate milk Monday night, poor fellow.
Metric Prefixes Counting Line:
____- - Giga - - Mega - - ______ hecto deca _____ deci ____ milli - - micro - - nano - - pico - - femto (The double dashes between some of the prefixes are place holders for "unnamed" decimal places. See below.
Count these dashes when moving the decimal.)
Base Units:
1.__________________
2.__________________
3.__________________
4.__________________
Metric Prefix Powers of Ten:
Tera - 1012
(missing 1011) (missing 1010) Giga - 109 (missing 108) (missing 107) Mega - 106 (missing 105) (missing 104) kilo - 103 hecto - 102 deca - 101 base unit - 100 deci - 10-1 centi - 10-2 milli - 10-3 (missing 10-4) (missing 10-5) micro - 10-6 (missing 10-7) (missing 10-8) nano - 10-9 (missing 10-10) (missing 10-11) pico - 10-12 (missing 10-13) (missing 10-14) femto - 10-15
Metric Prefix Abbreviations:
T - - G - - M - - k h da base unit d c m u - - n - - p - - f
Visit http://www.aaastudy.com/mea212x2.htm which has practice quizzes for more help.
Scientific Notation
Scientists abbreviate long numbers containing many zeros by using scientific notation. The notation can easily be recognized by the "x10" portion of the number. A superscript follows the "x10." Read below to understand the message communicated by the superscript.
____ x10 ___
The superscript can be either positive or negative.
If the superscript is positive, then the number represented is a LARGE number. To expand the notation into a more familiar form, the decimal will be moved to the right the number of spaces designated by the number of the superscript. This will place zeros behind the number making it large.
If the superscript is negative, then the number represented is a small number. To expand the notation into a more familiar form, the decimal will be moved to the left the number of spaces designated by the number of the superscript. This will place zeros in front of the number making it small.
2.3 x 10 4
The decimal will be moved 4 spaces to the right, which places zeros behind the 3.
23 000 2.3 x10 -4
The decimal will be moved 4 spaces to the left, which places zeros in front of the 2.
0.00023 Examples:
Calculators and Scientific Notation
Many students have learned to use the ^ button on calculators to insert superscripts or exponents. However, scientific calculators are created to handle scientific notation in a much easier way. Learning to use the calculator's functions will eliminate the need for parentheses and cut down on key strokes.
Graphing calculator: Find the "EE" button. It may be a 2nd function. The button takes the place of "x10"
in scientific notation. You'll not need to hit a ^ OR x10.
Non-graphing calculator: Find the "EXP" button or an "EE" button. Either of these buttons takes the place of "x10" in scientific notation. You'll not need to hit a ^ OR x10.
Example:
2.3 x 10 4
Should be entered as "2.3 EE 4" OR "2.3 EXP 4"
Notice that no X or 10 were entered.
Additional Resource:
Click here to visit the Norton ChemTour, and select chapter 1 Scientific Notation.
Significant Figures
What is a significant figure?
In laboratory and industry situations, measurement is common. Error occurs in measurements made by the human eye. Recording measurements requires scientists to understand the error involved, and significant figures provide a systematic process for presenting accurate measurements while clearly communicating the estimations or areas of possible error.
Example:
Let's compare these two measurements: 3.5 cm and 3.50 cm
3.5 cm = A scientist can deduce that the instrument's smallest marking was to the centimeter. The item being measured is DEFINITELY 3 cm long. The last digit communicates that it is estimated to be about halfway between 3 and 4 cm.
3.50 cm = A scientist can deduce that the instrument's smallest marking was to the tenth of a centimeter.
The item being measured is DEFINITELY 3 cm long, and it is DEFINITELY touching the fifth tenth of a centimeter marking after 3 cm. The last zero communicates that It is estimated to be exactly at the fifth tenth of a centimeter marking.
Conclusions:
More digits communicates more specific measurements made with more detailed instruments. The final digit in any measurement is an estimated digit reading one decimal place beyond the markings of the instrument.
How are significant figures incorporated into calculations?
Addition/Subtraction
1. Line up the decimals of the numbers.
2. Draw a vertical line at the end of the "shortest" number.
3. Add or subtract as usual.
4. Round the answer at the vertical line. The number to the right of the line will tell you whether to round up or down.
You must round the answer to the "shortest number," which is 9. This means that the answer cannot go beyond the ones place.
Examples:
If asked to add 3.458 + 23.789 + 9, then you'll need to write down the problem.
3.458 23.789 +9 36.247 = 36
Multiplication/Division
1. Count the number of significant figures in each of the numbers to be calculated.
2. Multiply or divide as usual.
3. Round the answer to the smallest number of significant figures. (Calculated answers can only be as specific as the LEAST specific measurement.)
You must count the significant digits in each number involved in the calculation. 3.458 has 4 sig figs, 23.789 has 5 sig figs, and 9 has only one sig fig. Therefore, 9 is the least specific measurement (having the lowest number of sig figs). Our answer can only have one sig fig as a result. We cannot round 740 off to 7...that doesn't make any sense...instead we add the 0 place holders to make a more reasonable rounding.
Examples:
If asked to multiply 3.458 x 23.789 x 9, then you'll need to write down the problem.
3.458 23.789 x 9
740.361258 = 700 Additional Resource:
Click here to: Visit the Norton ChemTour, and select Chapter 1 Significant Figures.
Density
Density = mass / volume
The idea is surprisingly simple: how much matter (stuff) is shoved into a space (volume). We're basically asking:
Is it crowded in there, or do you have lots of empty room?
Density Units
The units for density are "derived units." This means that they are similar to compound sentences in English class...they have two parts. The numerator for density will be a mass unit (gram, kilogram, etc.), and the
denominator will be a volume unit. The volume unit is the more complicated of the two. Volume can be measured and calculated as length x width x height, which results in a cubic unit (cm3, m3, etc), OR it can be measured using a graduated cylinder, which results in liters, milliliters, etc.
Density of Water
Water is one of the most common substances on Earth, and scientists have used it to define many ideas. Density is one of them. The idea of density was created using water as a reference. Every good chemistry student will commit to memory: Dwater = 1 g/mL. This means that 1 gram of water will take up exactly 1 mL of space in a graduated cylinder. Another important idea to know, the 1 mL of water will take up exactly 1 cm3 of space in three dimensions.
Density Examples:
1. What is the density of a substance that weighs 35.062 grams and fills a graduated cylinder to 23.50 mL?
D = mass / volume D = 35.062 g / 23.50 mL
D = 1.492 g/mL
2. If the density of liquid mercury is 13.6 g/cm3, what is the volume of 41.50 grams of the liquid?
D = mass / volume (13.6 g/cm3) = (41.50 g) / (X cm3) Use algebra to solve for the denominator.
HINT: Put a 1 under the density to create a proportion and cross multiply to find the answer.
(13.6 g/cm3)(X cm3) = (41.50 g) (1) (13.6 g/cm3) (13.6 g/cm3)
X = 3.05 cm3
Dimensional Analysis
In scientific measurements, dimensions are a fancy way to say "units." Dimensional analysis is a process of analyzing the units to find clues to help solve a problem. Units communicate about instruments used AND methods of calculation. We're going to learn to use them to provide help with calculating.
Specifically, units will confirm two paths:
1. The needed numbers/measurements to solve the problem 2. Whether to multiply or divide to solve the problem For example:
How many centimeter-wide tiles can be placed on a countertop that has been measured at 278.49 inches?
A relationship between centimeters and inches is needed
Inches need to be removed so that centimeters can be used in its place
Since 1 inch = 2.54 cm, the measured 278.49 inches should be multiplied by 2.54 cm and divided by 1 inch to cancel the inch unit and replace it with centimeter units.
The dimensional analysis will show:
Another example:
How many minutes will pass during a life span of 72.5 years?
A relationship between minutes and years is needed, but the average person doesn't memorize the number of minutes in a year.
Multiple relationships can be used to simplify the process: 60 min = 1 hr; 24 hr = 1 day; 365 days = 1 yr.
Since 72.5 years will start the dimensional analysis, 365 days should be multiplied (on top of the chart) and 1 yr will divide and cancel out the year units.
Additional Resource:
Click here to visit the Norton ChemTour, and select Chapter 1 Dimensional Analysis.
