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Chapter 5: Problem 78

Express each number in scientific notation. \(97,000 \times 10^{-11}\)

Short Answer

Expert verified
The scientific notation for \(97,000 \times 10^{-11}\) is \(9.7 \times 10^{-7}\).

Step by step solution

01

Expressing 97000 in the form a

To express \(97,000\) in a form \(a\), where \(1 \leq |a| < 10\), divide \(97000\) by \(10000\) to get \(9.7\). The factor \(10000\) can be written as \(10^4\), so we have \( 97000 = 9.7 \times 10^4 \).
02

Combining the Powers of 10

The given problem was \(97,000 \times 10^{-11}\), and we have just shown that \(97,000 = 9.7 \times 10^4\). Substituting \(97,000\) with \(9.7 \times 10^4\), the expression becomes \( (9.7 \times 10^4) \times 10^{-11} \). Using the rules of exponents, this simplifies to \(9.7 \times 10^{4-11} = 9.7 \times 10^{-7}\).

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(1.5,-3,6,-12, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=1000, r=1\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=-3\)

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

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=4, r=2\)
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