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Chapter 5: Problem 141

Give an example of a number for which there is no advantage to using scientific notation instead of decimal notation. Explain why this is the case.

Short Answer

Expert verified
The number 25 provides no advantage in using scientific notation. This is because it can be written as \(2.5 \times 10^{1}\), which doesn't make the number simpler or easier to read or understand than just writing 25.

Step by step solution

01

Select a Decent Sized Number

Choose a medium-sized number not requiring simplification. A number like \(25\) would suffice.
02

Convert to Scientific Notation

Change the selected number into scientific notation. In scientific notation, \(25\) would be written as \(2.5 \times 10^{1}\) or could also be written as \(25.0 \times 10^{0}\). As we see, it does not simplify the number nor does it make it easier to read.
03

Explanation

The rationale for this is that scientific notation is most beneficial for representing very large or very tiny numbers. The decimal number 25 is neither large nor tiny, and so writing it in scientific notation introduces unnecessary complexity while not making the number simpler to comprehend or manipulate algebraically.

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Most popular questions from this chapter

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=1,000,000, r=0.1\)

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