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Chapter 5: Problem 83

Perform the indicated operation and express each answer in decimal notation. \(\left(4.1 \times 10^{2}\right)\left(3 \times 10^{-4}\right)\)

Short Answer

Expert verified
The solution in decimal notation is \(0.123\).

Step by step solution

01

Multiply the significant figures

The significant figures in this case are \(4.1\) and \(3\). Their multiplication yields \(4.1 \times 3 = 12.3\).
02

Add the exponents

The operation \((4.1 \times 10^{2})\left(3 \times 10^{-4}\right)\) suggests that exponents of \(10^{2}\) and \(10^{-4}\) are present. These need to be combined by adding the exponents to each other. This results in \(10^{2-4} = 10^{-2}\).
03

Combine results

Now the multiplication of the significant figures and the result of the exponent addition have to be combined, yielding the solution in scientific notation: \(12.3 \times 10^{-2}\).
04

Convert to decimal notation

In order to express the solution in decimal notation, move the decimal point two places to the left (because of the negative sign in the exponent). This results in \(0.123\) as the final answer.

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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 \(a_{200}\), when \(a_{1}=60, r=1\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)

What is a sequence? Give an example with your description.

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(a_{1}=-70, d=-5\)
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