Read the Water Level With the Correct Number of Significant Figures.
Significant Figures
Information technology is important to exist honest when reporting a measurement, and so that information technology does not appear to be more than authentic than the equipment used to make the measurement allows. We tin reach this by controlling the number of digits, or significant figures, used to report the measurement.
Determining the Number of Meaning Figures
The number of significant figures in a measurement, such equally 2.531, is equal to the number of digits that are known with some degree of confidence (2, 5, and 3) plus the final digit (1), which is an estimate or approximation. As we improve the sensitivity of the equipment used to make a measurement, the number of meaning figures increases.
| Postage stamp Calibration | 3 �i thou | 1 significant figure | ||
| Two-pan residual | 2.53 �0.01 k | 3 meaning figures | ||
| Analytical balance | two.531 �0.001 m | 4 significant figures |
Rules for counting significant figures are summarized beneath.
Zeros within a number are always pregnant. Both 4308 and 40.05 contain four significant figures.
Zeros that practice nothing but ready the decimal point are not significant. Thus, 470,000 has two significant figures.
Trailing zeros that aren't needed to hold the decimal point are significant. For example, 4.00 has three significant figures.
If you lot are not sure whether a digit is significant, assume that it isn't. For example, if the directions for an experiment read: "Add the sample to 400 mL of water," presume the volume of water is known to i significant figure.
Improver and Subtraction with Significant Figures
When combining measurements with different degrees of accurateness and precision, the accuracy of the final answer can be no greater than the least authentic measurement. This principle tin be translated into a simple dominion for addition and subtraction: When measurements are added or subtracted, the respond can contain no more than decimal places than the least accurate measurement.
| 150.0 g HtwoO | (using pregnant figures) |
| + 0.507 yard salt | |
| 150.5 g solution | |
Multiplication and Division With Significant Figures
The same principle governs the use of significant figures in multiplication and segmentation: the final result tin be no more than accurate than the least accurate measurement. In this case, however, nosotros count the meaning figures in each measurement, not the number of decimal places: When measurements are multiplied or divided, the answer tin contain no more significant figures than the least accurate measurement.
Case: To illustrate this dominion, let's calculate the toll of the copper in an old penny that is pure copper. Let's assume that the penny has a mass of two.531 grams, that information technology is essentially pure copper, and that the price of copper is 67 cents per pound. We tin starting time by from grams to pounds.
We then apply the price of a pound of copper to calculate the price of the copper metallic.
There are four meaning figures in both the mass of the penny (ii.531) and the number of grams in a pound (453.six). But there are only two significant figures in the toll of copper, so the final respond tin only have 2 significant figures.
Rounding Off
When the answer to a calculation contains likewise many significant figures, it must exist rounded off.
In that location are 10 digits that can occur in the final decimal identify in a calculation. One style of rounding off involves underestimating the respond for five of these digits (0, 1, 2, 3, and 4) and overestimating the answer for the other five (5, 6, 7, 8, and nine). This approach to rounding off is summarized as follows.
If the digit is smaller than 5, driblet this digit and leave the remaining number unchanged. Thus, ane.684 becomes 1.68.
If the digit is five or larger, drop this digit and add one to the preceding digit. Thus, 1.247 becomes 1.25.
Units | Errors | Significant Figures | Scientific Notation
Dorsum to General Chemistry Topic Review
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Source: https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html
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