In the context of the scientific method, precision and accuracy have two distinctly different meanings.

The accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual (true)value.

The precision of a measurement system is the degree to which repeated measurements under unchanged conditions show the same results.

A measurement system can be accurate but not precise, precise but not accurate, neither, or both.

www.yorku.ca/psycho/en/pics_en/postscript_f1.gif

Significant figures are very important in science.

The significance of a digit has to do with whether it represents a true measurement or not.

Any digit that is actually measured or estimated will be considered significant.

Placeholders, or digits that have not been measured or estimated, are not considered significant.

1. Digits from 1-9 are always significant.

2. Zeros between two other significant digits are always significant

3. All final zeros to the right of the decimal place are significant.

4. Zeros used solely for spacing the decimal point (placeholders) are not significant (Unless specifically measured and noted with a line above the number).

Now, the letters "A" (decimal absent) and "P" (decimal present) also correspond to the "Atlantic" and "Pacific" Oceans on a map. Now, assume the top of the page is North, and imagine an arrow being drawn toward the number from the appropriate coast. Once the arrow hits a nonzero digit, it and all of the digits after it are significant.

Example 1. How many significant digits are shown in the number 20 400 ? Well, there is no decimal, so we think of "A" for "Absent". This means that we imagine an arrow coming in from the Atlantic ocean

20 400 this shows 3 significant numbers

as you do not count numbers until you hit a significant digit

Modified from http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm

Example 2. How many significant digits are shown in the number 0.090 ? Well, there is a decimal, so we think of "P" for "Present". This means that we imagine an arrow coming in from the Pacific ocean.

0.090 This shows that the number has two significant digits after the non zero number is encountered

Modified from http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm

Addition and subtraction with sig figs follows a special rule known as the “Least Precise Decimal.” Since significant figures are only as good as the level of precision used in measurement, the lowest level of precision dictates the significant figures.

This is much different than regular sig figs!!

Addition In the example, 2.02 has the least level of precision as it only reports numbers to the hundredth place. Therefore, significant figures can not be reported beyond this point.

Rounding rules:If the digit after the number to be rounded is >5, round the digit up.If the digit after the number to be rounded is <5, keep the number present.

In the special case where the digit following a rounding number is exactly 5 and no more, follow “banker’s rules” where the an odd number preceding the 5 is rounded up but an even number before the five stays the same.

http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html

Same rules as with addition – least precise decimal.

http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html

Multiplication and division go by the same standard rules as regular significant figures with the lowest number of sig. figs. determining how the answer is reported.

http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html

In a calculation that has multiple operations, keep track of how many significant digits you should have after each step, but don’t round off your answer until the very end of the calculation. It may help to write out each step and underline the extra digits that you keep.

Ex. [2.33 + 1.5]/123.1

= 3.83/123.1 (first step gives an answer with 1 decimal place which would give 2 significant digits in the numerator, remember this but use all of the digits in the next step)

= 0.03111 (2 significant digits were divided by 4 significant digits, so round to 2 significant digits) = 0.031

http://ux1.eiu.edu/~cfrp/1315SigFigs.htm