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Chapter 5: Problem 92

Perform the indicated operation and express each answer in decimal notation. \(\frac{9.6 \times 10^{-7}}{3 \times 10^{-3}}\)

Short Answer

Expert verified
The result of \(\frac{9.6 \times 10^{-7}}{3 \times 10^{-3}}\) expressed in decimal notation is \(0.00032\).

Step by step solution

01

Separate the numerical constants from the exponential parts

In the given expression, \(\frac{9.6 \times 10^{-7}}{3 \times 10^{-3}}\), separate the numerical constants \(9.6\) and \(3\) and the exponential parts \(10^{-7}\) and \(10^{-3}\). This gives us \(\frac{9.6}{3}\) and \(\frac{10^{-7}}{10^{-3}}\).
02

Perform the division operation with numerical constants

Divide the numerical constants, \(9.6\) and \(3\), to obtain \(\frac{9.6}{3} = 3.2\).
03

Division of exponentials

For the exponential parts, remember that to divide terms with the same base, you subtract the exponents. This means \(\frac{10^{-7}}{10^{-3}} = 10^{-7-(-3)} = 10^{-4}\).
04

Combine the results

Combine the results from step 2 and step 3 to get the final answer. Thus, \(\frac{9.6 \times 10^{-7}}{3 \times 10^{-3}}\) simplifies to \(3.2 \times 10^{-4}\).
05

Express in decimal notation

Express the result in decimal notation. With the result \(3.2 \times 10^{-4}\), knowing that \(10^{-4}\) represents the decimal point being moved four positions to the left, we rewrite this as \(0.00032\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3, \frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(2,6,10,14, \ldots\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sequence \(1,4,8,13,19,26, \ldots\) is an arithmetic sequence.

The sum, \(S_{n}\), of the first n terms of an arithmetic sequence is given by $$ S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right), $$ in which \(a_{1}\) is the first term and \(a_{n}\) is the nth term. The sum, \(S_{n}\), of the first \(n\) terms of a geometric sequence is given by $$ S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}, $$ in which \(a_{1}\) is the first term and \(r\) is the common ratio \((r \neq 1)\). Determine whether each sequence is arithmetic or geometric. Then use the appropriate formula to find \(S_{10}\), the sum of the first ten terms. \(4,10,16,22, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,-6,6,-6, \ldots\)
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