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.
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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