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Chapter 5: Problem 109

Perform the indicated computations. Express answers in scientific notation. \(\frac{\left(1.6 \times 10^{4}\right)\left(7.2 \times 10^{-3}\right)}{\left(3.6 \times 10^{8}\right)\left(4 \times 10^{-3}\right)}\)

Short Answer

Expert verified
The solution to the given calculation is \(8 \times 10^{-5}\).

Step by step solution

01

Multiply the coefficients and add the exponents

Start by multiplying the tops and the bottoms separately. Multiply the coefficients which are the numbers alone, and then add the exponents of ten. Thus, for the numerator, \(1.6 \times 7.2 = 11.52\). For the exponents, add \(4 + -3 = 1\), hence we have \(11.52 \times 10^{1}\). For the denominator, \(3.6 \times 4 = 14.4\). Again, add the exponents, \(8 + -3 = 5\), hence we have \(14.4 \times 10^{5}\).
02

Divide the coefficients and subtract the exponents

Next, divide the coefficient of the numerator by the coefficient of the denominator and subtract the exponent of denominator from the exponent of numerator. Thus, divide the coefficient 11.52 by 14.4 to get 0.8. Then, subtract 5 from 1 to get -4. The result is \(0.8 \times 10^{-4}\).
03

Adjust to correct scientific notation

Scientific notation generally has one digit to the left of the decimal point. Thus, we adjust by moving the decimal point one place to the right, resulting in the coefficient 8. Simultaneously, reduce 1 from the exponent to account for this move, yielding an exponent of -5. The final result is \(8 \times 10^{-5}\).

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Most popular questions from this chapter

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

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{1}{2}, 1, \frac{3}{2}, 2, \ldots\)

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

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,3, \frac{3}{2}, \frac{3}{4}, \ldots\)

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