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Dr. Walt Volland revised July 1, 2013 all rights reserved
Significant figures or digits are all the certain digits and the first digit that is uncertain. This means that since all measured numbers have an uncertainty the last digit reported is estimated and not know for sure. The illustration below shows what this means. The image shows a liquid thermometer in the twenty degree range. It is certain that the reading is between 24.0 and 25.0 degrees. There is an uncertainty in reading the first decimal place since it can only be estimated. The reading looks like it is 24.8. The measurement has three significant figures because the 2 and the 4 are known for certain, but the next digit can only be estimated to be 8 and could be either a 7 or a 9. The measured temperature with this uncertainty is best written as 24.8 +/- 0.1 degree. The actual value could be as low as 24.7 degree or as high as 24.9 degree. The last digit is uncertain. The measurement has 3 significant digits. |
Image of thermometer stem for measurement in the twenty degree range
Counting significant digits in scientific notation Significant digits for numbers written in exponential or scientific notation have a coefficient that includes only the significant figures in the measurement. For example the number 3.5 x 10-23 has only 2 significant figures. The number 9.41 x 105 would have three significant digits. The last number (digit) written is assumed to be an uncertain number. EXAMPLES: How many significant digits are in each of the following values?
Exact numbers Exact numbers are often used to convert one unit to another. They have no uncertainty. Exact numbers have an infinite number of significant figures. Definitions and counts are examples of exact numbers. Commonly exact numbers are used as conversion factors. Exact numbers are not measured values. EXAMPLES of exact numbers All of these are definitions.
All exact numbers are definitions.
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