Tuesday, 25 October 2011

Accuracy Vs. Precision and Sig Figs

Accuracy VS. Precision




Accuracy:

Is how close the measurement is to the actual accepted value!




Precision:

Is how reproducible the measurement is compared to other similar measures!





Significant Figures – Sig. Fig.

Significant figures simply are: how to write a math equation correctly!
The more precise a measurement is… it will result in more significant digits!

What are significant digits??? - They're significant figures

- They are the digits contained within a measurement up until the 1st uncertain digit which include every certain digit and 1 uncertain digit.

What are Certain and Uncertain Digits???

-          Certain digits are known to be correct without any margin for error; they should include all the digits up until the last digit
-          Uncertain digits may have a margin for error; they should be the last number contained within a given measurement.

For example:

8.27 mL ----> 8 and 2 are certain digits and the 7 is the uncertain digit.



0s:

When counting significant digits one may encounter zeros... so in order to count sig figs...

1.       Trailing zeros are never counted when there is not a # left of the decimal place:                            
2.       E.g. 0.000008 has 1 significant digit
3.       Trailing zeros are counted when there is a number left of the decimal place:                               E.g. 7.08 has 3 significant digits
4.       Trailing zeros without a decimal place aren’t ever counted:                                                             E.g. 5800 has 2 significant digits


Exact #s:

Some values can be written easily as a specific amount and therefore rounding is unnecessary!  These numbers have an infinite number of significant figures.
                                For example: 7 can be expressed as 7.00000…

The Rules of Rounding:


Like Mathematics, in Science we always round to the appropriate number of digits by following a set of rules that slightly differs from Math.

1.       If digit after position of rounding is >5 round up.
2.       If digit after position of rounding is <5 round down.
3.       If digit after position of rounding =5 and there are no more digits (not including 0) round up.
4.       If digit after position of rounding =5 and ends at that number round to the closest even digit.

The Rules of Adding and Subtraction:

-          Always round to the fewest number of decimal places of one of the values within the equation because it is the first uncertain digit.
For example:
19.08 + 2.6 = 21.7

The Rules of Multiplication and Division:

-          Always round to the least amount of significant figures.
For example: 7.89 x 2.1 = 16


For additional information on significant figures and more examples visit:






















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