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Chapter 1: Problem 70

Is the use of significant figures in each of the following statements appropriate? (a) The 2005 circulation of National Geo graphic 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. (\boldsymbol{d} ) ~ Y o u ~ c a l c u l a t e ~ y o u r ~ g r a d e ~ p o i n t ~ a v e r a g e ~ t o ~ b e ~ 3.87562

Short Answer

Expert verified
The use of significant figures in statements (a) and (b) is not appropriate, as they provide an unnecessarily precise count of circulation and population. It would be more suitable to round these numbers (e.g., 7.81 million and 5.30 million, respectively). For statement (c), the given percentage (0.621%) is appropriate as it may be relevant to have more precise data when dealing with percentages. However, in statement (d), the calculated grade point average should be rounded to two decimal points (3.88) based on common grading system practices.

Step by step solution

01

Statement (a): National Geographic circulation in 2005

The given circulation number is 7,812,564. This number implies that the count is precise down to the last reader. In this situation, however, there is no need for reporting such a high degree of precision. Circulations are usually given in whole numbers with a few leading digits being more significant. Appropriate significant figures: 7.81 million or 7,810,000.
02

Statement (b): Population of Cook County, Illinois, on July 1, 2005

The given population number is 5,303,683. Similar to statement (a), the population count does not need to be this precise. Population numbers are often approximate and generally rounded up to thousands or tens of thousands. Appropriate significant figures: 5.30 million or 5,304,000.
03

Statement (c): Percentage of the U.S. population with the surname Brown

The given percentage is 0.621%. While it may seem unnecessary to have three significant figures in this case, percentages are often reported with a decimal point. Given that the percentage deals with the count of people, being precise might be relevant. Appropriate significant figures: 0.621% (the original number is appropriate).
04

Statement (d): Grade point average calculation

The given grade point average is calculated to be 3.87562. A grade point average must not have that many significant figures since most grading systems themselves do not possess that level of precision. The grade point averages are typically reported up to two decimal points. Appropriate significant figures: 3.88.

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