What is the Metric System?
The "metric system" is a system of measurement used for day-to-day measurements throughout most of the world and for all scientific measuring. The original "metric system" was developed in France in the 1790's and was refined into the "International System" (Le Système International d'Unités) in 1960. The metric system consists of one base unit for every measurable quantity and uses a set of prefixes based on decimals of 10 to derive larger and smaller units from the base. Its name is from the Greek (métron, to measure).
Why do scientists use the Metric System?
Since science is international (there are no countries with borders when it comes to scientific knowledge) the metric system is used throughout the world so all scientists can understand measurements and data the same way. The metric system is based on divisibility by 10 so it makes scientific calculations easier. And it is the simplest system to use because there is only one unit of measurement (or base unit) for each type of quantity measured (length, mass, etc.). In chemistry we will use the following base units: meter (for length), gram (for mass or weight), liter (for volume) and Celsius (for temperature).
Why don’t we use the Metric System in the USA?
The liter is the unit for volume in the metric system so if you ever drank from a 2 liter soda bottle before you in fact did use the metric system. In 1971 the US government pronounced that by the year 1981 we would be a country of metric users. However, for many reasons which may include lack of education, lack of interest and pride we as a country still only use metric sparingly, unless you are in science class.
Decimal divisions of the Metric System
Prefix / Abbreviation / ValueGiga / G / 1 000 000 000 or 109
Mega / M / 1 000 000 or 106
kilo / k / 1000 or 103
The basic unit has no prefix / no prefix / 1
centi / c / 0.01 or 10-2
millli / m / 0.001 or 10-3
micro / µ / 0.000 001 0r 10-6
nano / n / 0.000 000 001 or 10-9
Converting Using Metric Units & Prefixes
In science things we measure can be very small or very big. Since it is generally easier to understand numbers without large amounts of zeros the metric system uses prefixes along with base units so numbers are easier to work with when doing calculations.
Example: the thing measured always stays the same but since 1 meter is the exact same thing as 100 centimeters; this means one centimeter is smaller than one meter SO you need more centimeters to equal the same measurement in meters
Metric Conversion (by moving the decimal point)
(notice the chart is written horizontally)
(1000) (100) (10) (1) (0.1) (0.01) (0.001) X X (1*10-6) X X (1*10-9)
Kilo Hecto Deca Deci Centi Milli Micro Nano
(k) (h) (da) (d) (c) (m) (µ)* (n)
1) Find the starting prefix on the chart
2) Find the ending prefix on the chart
3) Determine how to move from starting to ending prefix on the chart
4) Move the decimal point, of the number, the same direction and number of decimal spaces as you did to go from starting to ending prefix on the chart
5) Rewrite the number with the decimal in the new place and with the new prefix
Metric Conversion (doing math as per prefix)
(1000) (100) (10) (1) (0.1) (0.01) (0.001) X X (1*10-6) X X (1*10-9)
Kilo Hecto Deca Deci Centi Milli Micro Nano
(k) (h) (da) (d) (c) (m) (µ)* (n)
Numbers with Exponents & Variables…
Exponents are shorthand for repeated multiplication of the same thing by itself. Remember from your arithmetic days (or is that daze?) what 23 means? It means that three 2's are multiplied together 23=2·2·2=8. The thing that's being multiplied, the “2” in this example, is called the "base".
This process of using exponents is called "raising to a power", where the exponent is the "power". As you know, in algebra, we work with the unknown or variable x. The thing to remember is that an x is a number -- we just don't know which number. So, exponents work with variables too, for example, x3=x·x·x. And we can also put numbers and exponents together, for example, 5x3 = 5·x·x·x. Here the 5 is called a coefficient (because it's a number in front of the variable x) and it's multiplied in with the x's.
Exponents are used in Scientific Notation…
Because scientists often deal with very large and/or small numbers that contain lots of zeros; we use exponents to reformat these numbers to make calculations easier. To format in scientific notation write the first digit of the number (which must be 1-9) followed by the decimal point and then the rest of the digits of the number, the entire number is then multiplied by 10 raised to the appropriate power.
For example, to write 124 in scientific notation; first write "1.24". This is not the same number, but (1.24)(100) is, and since 100 = 102, the scientific notation format for 124 is written as 1.24·102 .
And, like the metric system, since we are multiplying by 10 we can convert by simply moving the decimal. To write 3.6·1012 in nonscientific format: since the exponent on 10 is positive, we need to move the decimal point to the right, in order to make the number LARGER and since the exponent on 10 is "12" we need to move the decimal point twelve places, so then put zeros
in and the number is 3,600,000,000,000.
To write 0.0000000000436 in scientific format, the number (as opposed to the ten-to-the-power) will be "4.36". So count how many places the decimal point has to move to get from where it is now to where it needs to be, , so then the power on 10 has to be “–11”.
"Eleven", because that's how many places the decimal point needs to be moved, and "negative", because we are dealing with a SMALL number. So, in scientific notation, the number is written as 4.36·10–11 .
Solving Basic Algebra Equations…
In general, to solve an equation for a given variable, you need to "undo" whatever math has been done to the variable in the equation. You do this in order to get the variable by itself; in technical terms, you "isolate" the variable. This results in "(variable) equals (some number)", where (some number) is the answer they're looking for.
For example, to solve x + 6 = -3, you want to get the x by itself; that is, you want to get "x" on one side of the "equals" sign, and some number on the other side. Since you want just x on the one side, this means that you don't like the "plus six" that's currently on the same side as the x. Since the 6 is added to the x, you need to subtract to get rid of it. That is, you need to subtract a 6 from the x in order to "undo" having added a 6 to it. This brings up the most important consideration with equations, whatever you do to the one side; you must do the exact same thing to the other side! Probably the best way to keep track of this subtraction of 6 from both sides is to format your work this way:
What you see here is that we've subtracted 6 from both sides, drawn an "equals" bar underneath both sides, and added down: x plus nothing is x, 6 minus 6 is zero, and –3 plus –6 is –9. The solution is the last line of your work: x = –9.
To Solve x – 3 = –5 since we want to get x by itself, we don't want the "–3" that's with the variable. The opposite of subtraction is addition, so we'll undo the –3 by adding 3 to both sides, and then adding down:
Then the solution is x = –2.
Ø The "undo" of multiplication is division. If something is multiplied on the x, we undo it by dividing both sides (that is, dividing each term on both sides) of the equation by whatever is multiplied on the x:
To Solve 2x = 5 since the x is multiplied by 2, we need to divide both sides by 2:
Warning: In science since we work with measurable quantities not
simply “numbers” all answers should be in decimal format!!!
So, the solution is x = 2.5.
Ø The "undo" of division is multiplication:
To Solve = –6 since the x is divided by 5, we’ll need to multiply both sides by 5:
Then the solution is x = –30.
Practice
The following websites can give you more review, sample problems, and interactive practice problems for each topic. REMEMBER the self-check strategy...try it first with NO HELP; if you are not getting the correct answers...go back and re-review and/or use a sample problem or conversion chart as a guide. BUT you won't have sample problems to follow during the test so make sure you can do problems without help. (There are many more web site resources for help; these are only a few good ones…)
The Centennial School District is not responsible for the content or the links on web pages not in the Centennial School District domain.
Metric System
http://www.aaamath.com/mea.html#topic50
http://www.themetricsystem.info/howtolearn.htm
Scientific Notation
http://www.nyu.edu/pages/mathmol/textbook/scinot.html
http://www.aaamath.com/dec71i-dec2sci.html
Algebra
http://www.math.com/practice/Algebra.html
http://www.aplusmath.com/Flashcards/algebra.html
http://www.321know.com/equ.htm#topic15
Metric System, Scientific Notation & Algebra Practice
Name: ______
Complete the following problems as per instructions. Do your own work in order to see what you need to review. Try to do the problems with no outside help as if this were a test.…questions will be graded for correctness and returned so you can make see what you did wrong and make corrections, get extra help, and practice more before the test.
The following problems range in difficulty from single skill basic to multiple skill problems for which you must put separately learned things together in order to solve for x:
a) x + 5 = 78 b) x - 4 = 8 c) x + 4 = 21
d) 36 - 6 = x + 5 e) 14 = 7 – x f) 64 = x + 12
g) 5x = 25 g) x ÷ 8 = 2 i) 12 = 24
x
j) 4x + 2x = 16 k) 3 - x = 4x l) x + 9 = 18 - 2x
m) x = 8 n) 6x - 2 + 2x = -2 + 4x + 8 o) 5x2 = 50
4 5
p) 2( 4 + 9x) = 20 q) -18 - 6x = 6(1 + 3x) r) 39 = 9.45
x - 6
s) x(3.5*1023) = 6.7*10-12 t) 1.032*10-4 + 4.35*10-3 = x + 3.54*10-3