Chapter 4.6, Problem 15E

i.

To determine

To identify: The quotient of the duration of a millisecond and the duration of nanosecond.

Answer to Problem 15E

The quotient of the duration of a millisecond and the duration of nanosecond is

  $\frac{{10}^{-3}}{{10}^{-9}}$

Explanation of Solution

Given information:

Given table,

  $\begin{array}{cc}\text{Name}\text{of}\text{unit}& \text{Duration}\\ \text{Millisecond}& {10}^{-3}\sec \\ \text{Microsecond}& {10}^{-6}\sec \\ \text{Nanosecond}& {10}^{-9}\sec \end{array}$

The duration of millisecond is ${10}^{-3}$ sec.

The duration of nanosecond is ${10}^{-9}$ sec.

Then,

The quotient is of the form

  $\frac{a}{b};b\ne 0$

So, the quotient of the duration of a millisecond and the duration of nanosecond is

  $\frac{{10}^{-3}}{{10}^{-9}}$

Conclusion:

The quotient of the duration of a millisecond and the duration of nanosecond is

  $\frac{{10}^{-3}}{{10}^{-9}}$

ii.

To determine

To identify: The solution of quotient

  $\frac{{10}^{-3}}{{10}^{-9}}$ .

Answer to Problem 15E

  $\frac{{10}^{-3}}{{10}^{-9}}={10}^6$

Explanation of Solution

Given information:

Quotient $\frac{{10}^{-3}}{{10}^{-9}}$ .

Concept Involved:

Use power formula,

  $\begin{array}{l}\frac{a^n}{b^m}=a^n{b}^{-m}\\ \text{and}\\ \frac{a^n}{a^m}=a^{n-m}\end{array}$

The quotient $\frac{{10}^{-3}}{{10}^{-9}}$ can be written as

  $\begin{array}{c}\frac{{10}^{-3}}{{10}^{-9}}={10}^{-3}{10}^{-\left(-9\right)}\\ ={10}^{-3}{10}^9\\ ={10}^{-3+9}\\ ={10}^6\end{array}$

Conclusion:

  $\frac{{10}^{-3}}{{10}^{-9}}={10}^6$