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Study Materials. Why use Doubtnut? Instant Video Solutions. Request OTP. This difference implies that the 4. A mass reported as 4. Thus, the mass might be anything between 3. Without further information, we cannot be sure whether the difference in uncertainties of the two measurements reflects the precision or the accuracy of the measurement. How many significant figures should be reported for this measurement? Answer: five, as in the measurement To determine the number of significant figures in a reported measurement, read the number from left to right, counting the digits starting with the first digit that is not zero.
In any measurement that is properly reported, all nonzero digits are significant. Because zeros can be used either as part of the measured value or merely to locate the decimal point, they may or may not be significant:.
Zeros between nonzero digits are always significant— kg four significant figures ; 7. Zeros at the beginning of a number are never significant; they merely indicate the position of the decimal point—0.
Zeros at the end of a number are significant if the number contains a decimal point—0. A problem arises when a number ends with zeros but contains no decimal point. In such cases, it is normally assumed that the zeros are not significant. Exponential notation Appendix A. For example, a mass of 10, g can be written to show three, four, or five significant figures depending on how the measurement is obtained:. In these numbers all the zeros to the right of the decimal point are significant rules 1 and 3.
The exponential term 10 4 does not add to the number of significant figures. How many significant figures are in each of the following numbers assume that each number is a measured quantity : a 4. If the number has more significant figures, a decimal point should be employed or the number written in exponential notation. Thus, How many significant figures are in each of the following measurements: a 3.
Answers: a four, b two, c three. When carrying measured quantities through calculations, the least certain measurement limits the certainty of the calculated quantity and thereby determines the number of significant figures in the final answer. The final answer should be reported with only one uncertain digit.
To keep track of significant figures in calculations, we will make frequent use of two rules, one for addition and subtraction, and another for multiplication and division. For addition and subtraction , the result has the same number of decimal places as the measurement with the fewest decimal places.
When the result contains more than the correct number of significant figures, it must be rounded off. Consider the following example in which the uncertain digits appear in color:. For multiplication and division , the result contains the same number of significant figures as the measurement with the fewest significant figures.
For example, the area of a rectangle whose measured edge lengths are 6. Notice that for addition and subtraction, decimal places are counted in determining how many digits to report in an answer, whereas for multiplication and division, significant figures are counted in determining how many digits to report.
In determining the final answer for a calculated quantity, exact numbers are assumed to have an infinite number of significant figures.
Thus, rounding 7. Rounding 4. The width, length, and height of a small box are Calculate the volume of the box, using the correct number of significant figures in your answer. In reporting the volume, we can show only as many significant figures as given in the dimension with the fewest significant figures, that for the height two significant figures :.
A calculator used for this calculation shows Because the resulting number is , it is best reported in exponential notation, 2. It takes Calculate her average speed in meters per second, and express the result to the correct number of significant figures.
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