Chapter 9, Problem 11STP

(a)

To determine

To calculate:To write width of the cotton fiber as a fraction when width is given as −

  $0.001$$cm$

Answer to Problem 11STP

The width of the cotton fiber in fraction is $\frac{1}{1000}$$cm$

Explanation of Solution

Given information:

Given width of the cotton fiber is $0.001$$cm$

Formula Used:

To convert a decimal into fraction, divide the number in the powers of $10$ , where power is the number of values after decimal.

Calculation:

Given expression is $0.001$

Using the above explanation, we have:

  $0.001=\frac{1}{1000}$

Thus, the width of the cotton fiber in fraction is $\frac{1}{1000}$$cm$

Conclusion:

The width of the cotton fiber in fraction is $\frac{1}{1000}$$cm$

(b)

To determine

To calculate: To write width of the cotton fiber as a negative exponent when width is given as −

  $0.001$$cm$

Answer to Problem 11STP

The width of the cotton fiber in negative exponent is ${10}^{-3}$$cm$

Explanation of Solution

Given information:

Given width of the cotton fiber is $0.001$$cm$

Formula Used:

Exponent formula:

  $\frac{1}{a^m}=a^{-m}$

Calculation:

Given expression is $0.001$

Using the above explanation, we have:

  $\begin{array}{l}0.001=\frac{1}{1000}\\ 0.001=\frac{1}{{10}^3}\\ 0.001={10}^{-3}\end{array}$

Thus, the width of the cotton fiber in negative exponent is ${10}^{-3}$$cm$

Conclusion:

The width of the cotton fiber in negative exponent is ${10}^{-3}$$cm$

(c)

To determine

To calculate: To find the number of the cotton fibers needed to make a stack of length $5$ cm when width is given as −

  $0.001$$cm$

Answer to Problem 11STP

The number of the cotton fibers needed to make a stack of length $5$ cm is $5000$ .

Explanation of Solution

Given information:

Given width of the cotton fiber is $0.001$$cm$

Calculation:

Given expression is $0.001$

To find the number of the cotton fibers needed to make a stack of length $5$ cm, divide the total width by the width of each fiber:

  $\frac{5}{0.001}$

Solving the above expression, we have:

  $\begin{array}{l}\frac{5}{0.001}=\frac{5}{{10}^{-3}}\\ \frac{5}{0.001}=5\times {10}^3\\ \frac{5}{0.001}=5000\end{array}$

Thus, the number of the cotton fibers needed to make a stack of length $5$ cm is $5000$ .

Conclusion:

The number of the cotton fibers needed to make a stack of length $5$ cm is $5000$ .