Chapter 1, Problem 156QP

Which of the following has the largest mass?

$\begin{array}{l}\text{A}\text{.}\text{4}\text{.1}\times {\text{10}}^{-\text{2}}\text{kg}\\ \text{B}\text{.}\text{1}\text{.8}\times {\text{10}}^{\text{4}}\text{mg}\\ \text{C}\text{.}\text{25 g}\\ \text{D}\text{. 6}\text{.5}\times {10}^6\text{μg}\\ \text{E}\text{.}\text{7}\text{.6}\times {\text{10}}^{-1}\text{ g}\end{array}$

Arrange these quantities in order of increasing mass.

Interpretation Introduction

Interpretation:

The arrangement in the increasing order of the given measurements is to be discussed

Concept Introduction:

The amount of matter that exists in a body is known as mass. The SI unit of mass is kilogram(kg). This value is also measured in grams, pounds, tonnes, and many more by using the conversion factors of each of the units.

Answer to Problem 156QP

Solution:

The largest mass among all the given measurements is A $4.1\times {10}^{-2}\text{ kg}$ which is equal to $41\text{ g}$ .

The increasing order of the given measurements is $\text{E}<\text{D}<\text{B}<\text{C}<\text{A}$ .

Explanation of Solution

Given Information: The given measurements are as follows:

$4.1\times {10}^{-2}\text{ kg , 1}\text{.8}\times {10}^4\text{ mg , 25 g , }6.5\times {10}^6\text{ μg , }7.6\times {10}^{-1}\text{ g}$ which are named as A, B, C, D, E, respectively.

:

The units of all the measurements should be equal to compare and arrange them in the increasing order.

The conversion of $4.1\times {10}^{-2}\text{ kg}$ to $\text{g}$ .

The relation between kilogram $\left(\text{kg}\right)$ and gram $\left(\text{g}\right)$ is shown below:

$1\text{ kg}=1000\text{ g}$

The conversion factor used to convert $\text{kg}$ into $\text{g}$ is shown below:

$\frac{1\text{ kg}}{1000\text{ g}}\text{or}\frac{1000\text{ g}}{1\text{ kg}}$

$4.1\times {10}^{-2}\text{ kg}$ is converted into $\text{g}$ using conversion factor is shown below.

$\begin{array}{c}4.1\times {10}^{-2}\text{ kg}=4.1\times {10}^{-2}\text{ kg}\times \frac{1000\text{ g}}{1\text{ kg}}\\ =4.1\times {10}^1\text{g}\\ =41\text{ g}\end{array}$

Therefore, $4.1\times {10}^{-2}\text{ kg}$ is equal to $41\text{ g}$ .

The conversion of $\text{1}\text{.8}\times {10}^4\text{ mg}$ to $\text{g}$ .

The relation between gram $\left(\text{g}\right)$ and milligram $\left(\text{mg}\right)$ is shown below:

$1\text{ g}=\text{1000 mg}$

The conversion factor used to convert $\text{mg}$ into $\text{g}$ is shown below:

$\frac{1\text{ g}}{1000\text{ mg}}\text{or}\frac{1000\text{ mg}}{1\text{ g}}$

$\text{1}\text{.8}\times {10}^4\text{ mg}$ is converted into $\text{g}$ using conversion factor is shown below.

$\begin{array}{c}\text{1}\text{.8}\times {10}^4\text{ mg}=\text{1}\text{.8}\times {10}^4\text{ mg}\times \frac{1\text{ g}}{1000\text{ mg}}\\ =1.8\times {10}^1\text{g}\\ =18\text{ g}\end{array}$

Therefore, $\text{1}\text{.8}\times {10}^4\text{ mg}$ is equal to $18\text{ g}$ .

The conversion of $6.5\times {10}^6\text{ μg}$ to $\text{g}$ .

The relation between microgram $\left(\text{μg}\right)$ and gram $\left(\text{g}\right)$ is shown below:

$1\text{ μg}={10}^{-6}\text{ g}$

The conversion factor used to convert $\text{μg}$ into $\text{g}$ is shown below:

$\frac{1\text{ μg}}{{10}^{-6}\text{ g}}\text{or}\frac{{10}^{-6}\text{ g}}{1\text{ μg}}$

$6.5\times {10}^6\text{ μg}$ is converted into $\text{g}$ using conversion factor is shown below.

$\begin{array}{c}6.5\times {10}^6\text{ μg}=6.5\times {10}^6\text{ μg}\times \frac{{10}^{-6}\text{ g}}{1\text{ μg}}\\ =6.5\times 1\text{ g}\\ =6.5\text{ g}\end{array}$

Therefore, $6.5\times {10}^6\text{ μg}$ is equal to $6.5\text{ g}$ .

The final measurements are $41\text{ g}$ , $18\text{ g}$ , $25\text{ g}$ , $6.5\text{ g}$ , and $7.6\times {10}^{-1}\text{ g}$ .

The increasing order of the measurements is as follows:

$7.6\times {10}^{-6}\text{ g}<6.5\text{ g}<18\text{ g}<25\text{ g}<41\text{ g}$

The increasing order is as follows:

$\text{E}<\text{D}<\text{B}<\text{C}<\text{A}$

The largest mass among all measurements is A $\left(41\text{ g}\right)$ .

Therefore, the increasing order of the given measurements is $\text{E}<\text{D}<\text{B}<\text{C}<\text{A}$ .

Conclusion

The increasing order of the given measurements is $\text{E}<\text{D}<\text{B}<\text{C}<\text{A}$ .