Measured Digits:
* Result of a measurement: They are obtained by using a measuring tool (ruler, scale, thermometer, etc.).
* Always have some uncertainty: No measurement is perfectly precise. There's always a small margin of error due to the limitations of the instrument and human error.
* Significant figures matter: The number of digits you write down reflects the precision of your measurement. For example, if a ruler is marked in millimeters, you can only measure to the nearest millimeter, so your measurement will have a certain number of significant figures.
Exact Numbers:
* Defined or counted: They are not the result of a measurement, but rather come from definitions or counting.
* No uncertainty: They have no margin of error.
* Not limited by significant figures: They can be considered to have an unlimited number of significant figures.
Examples:
* Measured: The length of a table measured with a ruler might be 1.23 meters. This has three significant figures because the measurement was made to the nearest centimeter.
* Exact: There are exactly 12 eggs in a dozen. This is a definition, not a measurement, and has no uncertainty.
Why the Difference Matters:
Understanding the difference between measured and exact numbers is crucial for carrying out calculations involving measurements. When performing operations like addition, subtraction, multiplication, and division, you must consider the number of significant figures in your measurements to ensure your answer reflects the appropriate level of precision.
In summary:
* Measured digits: Uncertain, reflect the precision of the instrument.
* Exact numbers: Defined or counted, have no uncertainty.
