Significant Figures
Significant figures provide us with information about how good a measurement is. Generally, when you record a measurement using a piece of equipment, you should write all of the digits that you obtained directly or know for certainty from the measuring device and then add a final estimated or uncertain digit. As an example, if you have a ruler with markings at each centimeter, you would record a measurement to the centimeter marking as a certain digit plus one decimal place that you are estimating. (See here for more info about using a measuring device and recording a measurement to the correct number of signficant figures.)
Rules for Writing Significant Figures:
1) All digits other than zero are significant. For example, “4.3 grams” has two significant figures.
2) Zeros that are “sandwiched” between nonzero digits are significant. For example,“4.03 grams” has three significant figures.
3) Zeros written to the left of all nonzero digits “leading zeroes” are not significant. For example, “0.0043 grams” has two significant figures.
4) “Trailing zeroes” at the end of a number are not significant except if a decimal point is written in the number. A zero that is after a significant figure AND after a decimal is a significant zero. For example, “1000 grams” has one significant figure because the zeroes at the end are trailing zeroes. This value indicates that the measurement was rounded off to the nearest thousand grams. Compare this to “1000.0 grams” which has five significant figures and represents a measurement rounded to the nearest tenth of a gram.
5) When a number is written in scientific notation, the significant figures are the part of the number that’s before the “x 10n” portion. For example, “3.40 x 105 grams” has three significant figures.
Rules for Using Significant Figures in Calculations:
1) When adding or subtracting, the answer should be rounded to the least accurate decimal place. For example, 4.4 + 4.023 = 8.423 This rounds off to 8.4. The number 4.4 was only accurate to one decimal place, so the answer can only be accurate to one decimal place. Take away message: When adding or subtracting, round to the least number of decimal places.
2) When multiplying or dividing, the answer should have the same number of significant figures as the value with the fewest significant figures. For example, 1.330 x 3.8740 = 5.15242 Round this answer to 5.152, because 1.330 has only four significant figures. Take away message: When multiplying or dividing, round to the least number of significant figures.
Watch the video below to help you get a better understanding of significant figures:
Try the Significant Figures Practice Problems linked below: