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Chapter 1: Problem 4

What is(are) the difference(s) between 3.0 and \(3.0000 ?\) a) 3.0000 could be the result from an intermediate step in a calculation; 3.0 has to result from a final step. b) 3.0000 represents a quantity that is known more precisely than 3.0 c) There is no difference. d) They convey the same information, but 3.0 is preferred for ease of writing

Short Answer

Expert verified
a) Both numbers are common results in intermediate or final steps of calculations. b) 3.0000 represents a quantity that is known more precisely than 3.0. c) There is no difference. d) Both numbers convey the same information, but in different ways. Answer: b) 3.0000 represents a quantity that is known more precisely than 3.0.

Step by step solution

01

Compare the numerical values

First, let's look at the numerical values represented by 3.0 and 3.0000. Both numbers have the same value, which is 3. Now let's analyze the rest of the given options.
02

Verify if the numbers result from intermediate or final steps

We can't determine if the numbers come from an intermediate or final step in a calculation. Both 3.0 and 3.0000 can be a part of either step in the calculations. Thus, the option (a) is incorrect.
03

Compare precision

The greater the number of decimal places, the more precise the value appears. In this case, 3.0000 has four decimal places, while 3.0 has only one decimal place. Thus, 3.0000 indicates a higher precision than 3.0. Option (b) is correct.
04

Analyze the remaining options

As we have determined that there is a difference in precision, we can confirm that option (c) stating "There is no difference." is incorrect. Furthermore, option (d) is partially correct, as both numbers do convey the same information but with different levels of precision. In conclusion, the correct answer is: b) 3.0000 represents a quantity that is known more precisely than 3.0

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