Unit 1 Metric system, significant figures, factor label ...



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 1000

Hecto 100

Deka 10

Milli 1/1000

Centi 1/100

Deci 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.

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 = 81.3 centimeters

1.0 inches

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 = 118.25 ml or 120ml at 2sig figs

2 cups 2 pt 1 qt

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 = Observed value - Accepted value

Accepted value

Or % error = O - A

A

Precision – how reproducible your work is, are you consistent?

Trial average deviation

1. 3.40 ( 3.45 = .05 absolute deviation of trial # 1

2. 3.45 ( 3.45 = .00 absolute deviation of trail #2

3. 3.50 ( 3.45 = .05 absolute deviation of trial #3

3 (3.45 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.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download