Is the use of significant figures in each of the following statements appropriate? (a) The 2005 circulation of National Geographic was \(7,812,564 .\) (b) On July 1, 2005, the population of Cook County, Illinois, was $5,303,683 .(\mathbf{c})\( In the United States, \)0.621 \%$ of the population has the surname Brown. (d) You calculate your grade point average to be \(3.87562 .\)

Short Answer

Expert verified
For each statement: (a) The use of significant figures in the National Geographic circulation statement is appropriate since the circulation is a countable quantity. (b) The use of significant figures in the population of Cook County statement is appropriate as population should be reported with all significant figures for accuracy. (c) The use of significant figures in the percentage of Brown surnames statement is not appropriate; it would be better to round the percentage to one or two decimal places, e.g., \(0.62\%\) or \(0.621\%\). (d) The use of significant figures in the GPA calculation statement is not appropriate; it is recommended to round the value to one or two decimal places, e.g., \(3.88\) or \(3.9\).

Step by step solution

01

(a) National Geographic Circulation

In this statement, the given circulation number is \(7,812,564\). All non-zero digits (7, 8, 1, 2, 5, and 4) are considered significant figures. Since the circulation is a countable quantity, it is appropriate to use all the significant figures.
02

(b) Population of Cook County, Illinois

The population of Cook County, Illinois, is given as \(5,303,683\). Similarly as in the first case, all non-zero digits (5, 3, 6, and 8) are considered significant figures. When dealing with population, we need to maintain accuracy, and it is typical to report populations with all their significant figures.
03

(c) Percentage of Brown surnames in the United States

In this statement, \(0.621\%\) of the population has the surname Brown. Percentages are not countable quantities, and using the three significant figures as provided may not be appropriate. When dealing with percentages, it is usually better to round the number to one or two decimal places for easier comprehension and interpretation. So, it would be more appropriate to report the percentage as \(0.62\%\) or \(0.621\%\), depending on the desired precision.
04

(d) Grade Point Average Calculation

The stated grade point average (GPA) is \(3.87562\). GPAs are usually calculated based on a scale, such as from 0 to 4, and this number has many decimal places, which suggests a very high level of precision. In general, GPAs should be reported with one or two decimal places only (e.g., \(3.88\) or \(3.9\)) for better interpretation and communication. Using the given value with five decimal places is not appropriate, and rounding to a fewer decimal places is recommended.

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