Significant Figures

Who cares?

Sig Figs measure the degree of precision of a

measurement.

But first: What’s the difference between accuracy and precision?

Do they mean the same thing?

Important definitions:

• accuracy: a measure of how closely a measurement agrees with the correct or true value

• precision: a measure of how closely individual measurements agree with one another

Example question:Two students measured the mass of a small pebble,

which had an actual mass of 2.35 grams.

Sally’s measurements were 2.78 grams, 2.82 grams, and 2.81 grams.

Madison’s measurements were 2.30 grams, 2.34 grams, and 2.41 grams.

Which student was more accurate?Which student was more precise?

A correctly precise measurement includes all

digitsthat are knownfor sure, plus a

digit that isestimated.

For example:

Another example:

Rules for counting sig figs:

There are ONLY two rules to remember when counting

the # of Sig Figs.

Rule #1: Don’t start counting till you get to a number that isn’t a zero.

Rule #2: Once you start counting, don’t stop till you’ve counted all the

digits, including zeroes.

And you need to remember a little geography:

Where is the Atlantic Ocean, and where is the Pacific Ocean?

How many sig figs are in this number: 273.5200?

Ask yourself:

Is the decimal point present or absent?

Answer: PresentCount from first non-zero

number starting at the Pacific side.

273.5200

Once you start counting, you don’t stop!

Examples2.55 3 S.F.0.2500 4 S.F.100.25 5 S.F.

Examples12.500.00500.0003

The first step is always to ask yourself:

Is the decimal point present or absent?

18,000,000

Answer: AbsentCount from first non-zero number

moving from the Atlantic side.

18,000,000

Examples135 3 S.F.100 1 S.F.10500 3 S.F.

Examples

350 0.0020

17,500 27.02

135.0 2060

Using sig figs in

calculations

Formultiplication

and division:

Your answer can not be more

precise than the least precise

measurement.

Think of Sloppy Joe

You and your lab partner, Sloppy Joe, have been assigned to find the area of your lab table. You carefully measure the length, and find it to be 233.65 cm. Sloppy Joe casually slides the meter stick along the width, suggests that it measures about 200 cm.

233.65 x 200 = 46730

5 S.F. 1 S.F. 4 S.F.?

Answer must be recorded as 50,000 cm2

It can have only one sig fig.

Your answer MUST

have the same number

of sig figs as the factor with the least

number of sig figs.

610 x 6.20 = 3782

2 S.F. 3 S.F.What is the correct answer?

3800

Example: You calculate the density of an object with mass of

24.300 grams, and volume of 62.5 ml. How many sig figs in

your answer? D=M/V

24.300/62.5 = 0.3888Correct Sig. Figs. = 0.389

Foraddition and

subtraction

Your answer can not contain more decimal places than the least

precise measurement.

Line up the decimal points in

the numbers.2.515 + 1.3 +12.00

=????

2.5151.3

+ 12.0015.815

Answer stops here

Scientific notation

The number of sig figs comes from the number written before the times sign.

Examples3.50 x 1023 3 S.F.

5.0 x 10 -4 2 S.F.

3 x 10-4 1 S.F.