Significant Figures

Mr. Nelson – 2010

Uncertainty The pin is ½ way between the smallest lines on

the ruler – what do we do?

•We have to IMAGINE that there are 10 more spaces between those smallest lines and ESTIMATE

•We can see it is between the 2.8 and 2.9 mark, but…

•We can estimate visually that it is probably around 2.85 cm

Uncertainty•We can estimate visually that it is probably around 2.85 cm

•This is just a visual estimation though – that last number is uncertain – it could just as easily be 2.84 or 2.86 cm!!

•Note that the first two numbers in that measurement are always the same – just the last number, the estimated number, is uncertain

Rules for uncertainty

When making a measurement, record all numbers that are known, plus ONE uncertain digit.

These numbers (all certain numbers + 1 uncertain number) are called significant figures

Sig Fig Rules

****Nonzero integers are always significantExample: 1457 has four nonzero integers and four significant figures

1. When 0’s are between sig. figs., 0’s are always significant Example: 101 has 3 sig. fig. and 34055 has 5 sig. fig

2. When the measurement is a whole number ending with 0’s, the 0’s are never significant Example: 210 has 2 sig. figs. and 71,000,000 also has 2 sig. figs

3. When the measurement is less than a whole number, the 0’s between the decimal and other significant numbers are never significant (they are place holders). 

Example: .0021 has 2 sig. fig. and .0000332 has 3 sig. fig.

4. When the measurement is less than a whole number and the 0’s fall after the other significant numbers, the 0’s are always significant

Example: .310 has 3 sig. fig. and .3400 has 4 sig. fig

5. When the measurement is less than a whole and there is a 0 to the left of the decimal, the 0 is not significant. Example: 0.02 has only 1 sig. fig. and 0.110 has 3 sig. fig.

6. When the measurement is a whole number but ends with 0’s to the right of the decimal, the 0’s are significant.

 Example: 20.0 has 3 sig. fig., 18876.000 has 8 sig. fig.

Example Problems

Give the # of significant figures in each measurement:

1. A sample of orange juice contains 0.0108 g of vitamin C

2. A forensic chemist in a crime lab weighs a single hair and records its mass as 0.0050060g

3. The distance between two points is found to be 5.030x103 ft.

Rounding Rules

1. If the number you want to “round off” is less than 5, then the preceding digit stays the same

2. If that number is more than 5, round the preceding number UP.

3. ALWAYS wait till the end to round off numbers – don’t round as you go or your # might be off!

Rounding Examples

Round 4 321 211 to 4 sig figs

Round 2.35x10 to 2 sig figs

Round 0.003456 to 2 sig figs

Sig Figs in Calculations

2. For addition or subtraction: the limiting number is the one with the smallest number of decimal places.

Example: 12.00 + 18.0 + 1.013 = ?

Example: 0.6875 – 0.1 = ?

Sig Figs in Calculations

4. For multiplication and division:

the number of sig figs in your answer is the same as the SMALLEST number of sig figs (total) in the problem (this is the limiting measurement).

Example: 4.56 x 1.4 = 6.384 how do we do sig figs?

Example: 2.315 x 1.0 x 100 = ?

Note: for multiplication & division, sig figs are counted.

For addition & subtraction, the numbers to the right of the decimal place are counted.

Precision vs. Accuracy

Accuracy is telling the truth . . .

Precision is telling the same story over and over again.

Accuracy: the degree of conformity with “the truth”

Precision & accuracy, cont’d.

Precision: the quality, uniformity, or reproducibility of a measurement.

Note that this has nothing to do with how “true” the result is, just whether or not you can repeat it exactly.

Precision vs. Accuracy, cont’d.

Accuracy with precision: the person shooting these arrows has performed both accurately (on the bull’s eye) and precisely (over and over)

Precision vs. Accuracy, cont’d.

Precision with blunder – because all of your other results are accurate and precise, it is easy to see the “bad” data and toss it out.

•Accuracy with blunder – although this is accurate, it is not as precise – it may be easier to overlook the error

Percent Error

Accepted Value – Experimental Value x 100 = %

Accepted Value