Unit 1 Metric system, significant figures, factor label, accuracy
And precision
Metric system
Length - the meter, which is about three feet.
Volume - the liter, one tenth of a meter cubed. Or one cubic decimeter
Which is a little over a quart.
Mass - the kilogram, is the mass of one liter of water at standard temperature.
Prefixes
Kilo
Hecto
Deka
Milli
Centi
Deci
1000
100
10
1/1000
1/100
1/10
A kilo-gram is 1000 grams and a milli-gram is 1/1000 of a gram.
Significant figures Is a method of keeping track of how well or how poorly something
was measured. They are very important in good science.
When you measure something the last number you record is always an estimated
number. Then when you do calculations using these numbers the calculator
Assumes they are exact and spits out a number with many more decimal places
Than you really measured. It lies. In good science we don’t exaggerate the true.
Therefore we use the system of Sig Figs to control the exaggeration.
Sig Fig Rules
Significant figures are all the numbers you know for sure plus one
you are unsure of. (Estimated).
1. All non-zero numbers are significant.
2. Zeroes between two non-zero numbers are significant
207
The (0) is significant
3. Zeroes to the right of a non-zero number and to the left of an understood
Decimal are not significant. In the number 2000 with no decimal actually
written, the three zeroes are only placeholders to show the magnitude of the
number.
4. Zeroes to the right of a decimal and to the left of a non-zero number are
Not significant. In .0046 the two zeroes are not significant. They are only
place holders.
5. Zeroes to the right of a decimal and to the right of a non-zero number
Are significant. In 31.00 the zeroes are significant, because the number was
Measured to the hundredth place.
Math with Sig Figs
1. When multiplying ,your answer can only have the same number of
Sig figs as the least significant factor multiplied.
2.46 x
3.8 = 9.348 which becomes 9.3
2.46 is 3 SIG figs and 3.8 is only 2 sig figs, so you round the answer to
two sig figs, which is 9.3. The calculator implies that you measured
better than you really did.
2. Same rule applies to division
3. When adding ,you may keep your answer to the last decimal place that
You know all the added numbers to.
21.765
3.45
+ 2.842
28.057 The calculator assumes the digit after the 5 in 3.45 is a zero.
But it could be any thing from 1 to 9, therefore the seven in
Thousands place of the answer is bogus. And is only used to
Round the final answer to 28.06
4.Subtracting, follow the same rule as addition.
Factor label problem solving
Your in Europe and need to buy a new belt, your waist is 32 inches, but all the belts are
labeled in centimeters. What size do you buy?
32.0 inches x 2.54 centimeters
1.0 inches
=
81.3 centimeters
Note that the inches in the equation cancel out and you are left with centimeters.
.50 cups is how many milliliters?
.50 cups x 1 pint x 1 qt x 946 ml
2 cups
2 pt
1 qt
= 118.25 ml or 120ml at 2sig figs
Again note that cups pints and quarts all cancel out leaving only milliliters.
We will do most of our math this way! And you must show the work on paper or you
Get no credit, even if the answer is correct! We are developing our communication
skills.
Accuracy – how close you come to an accepted value.
Also called percent error
Percent error =
Or
Observed value - Accepted value
Accepted value
% error = O - A
A
Precision – how reproducible your work is, are you consistent?
Trial
1. 3.40
2. 3.45
3. 3.50
3 3.45
average



3.45
3.45
3.45
deviation
=
=
=
.05 absolute deviation of trial # 1
.00 absolute deviation of trail #2
.05 absolute deviation of trial #3
3.033
.033 is the averge deviation
for the three trials
This tells your boss how good you are when there is no accepted value to work with.