Significant figures (also known as significant digits or sig figs) are a way of expressing the precision of a measurement or a number. They are the meaningful digits in a measured or calculated value and are used to indicate the degree of certainty in the measurement. Significant figures are important in scientific and engineering calculations because they help convey the precision of the data being used.
Significant Figures Rules
Here are some rules and guidelines for determining and using significant figures:
- Non-zero digits (1-9) are always significant. For example, in the number 123.45, all the digits (1, 2, 3, 4, and 5) are significant.
- Any leading zeros (zeros to the left of the first non-zero digit) are not considered significant. For example, in the number 0.00456, only the digits 4, 5, and 6 are significant.
- Captive zeros (zeros between significant figures) are always significant. For example, in the number 10.05, all the digits (1, 0, 0, and 5) are significant.
- Trailing zeros (zeros to the right of the last non-zero digit) are considered significant only if there is a decimal point in the number. For example:
- In the number 100, the trailing zeros are not considered significant.
- In the number 100.0, all digits are significant.
- In measurements, the last digit is the estimated digit, and its uncertainty is expressed by the number of decimal places. For example, if you measure the length of an object with a ruler marked in millimeters, your measurement might be 23.4 mm, with one estimated digit.
- In addition and subtraction, the result should be rounded to the least number of decimal places in the original numbers. For example, if you add 12.345 and 3.2, the result should be rounded to one decimal place (15.5).
- In multiplication and division, the result should be rounded to the least number of significant figures in the original numbers. For example, if you multiply 3.456 and 12.1, the result should be rounded to three significant figures (41.7).
Significant figures are essential for maintaining the integrity of measurements and calculations. They help convey the precision and reliability of data, and they ensure that calculated results are consistent with the quality of the input data. When working with scientific data, it’s important to pay attention to significant figures to avoid misleading or inaccurate conclusions.