Chapter 1, Problem 1.100E

Do the following metric system conversions by changing only the power of $10$. For example, convert $2.5\text{L}$ to $\text{mL}$: $2.5\text{L}=2.5\times {10}^3\text{mL}$

a. Convert $4.5\text{km}$ to $\text{mm}$

b. Convert $6.0\times {10}^6\text{mg}$ to $\text{g}$

c. Convert $9.86\times {10}^{15}\text{m}$ to $\text{km}$

d. Convert $1.91\times {10}^{-4}\text{kg}$ to $\text{mg}$

e. Convert $5.0\text{ng}$ to $\text{mg}$

Interpretation Introduction

(a)

Interpretation:

The metric system conversion of the given quantity by changing only the power of $10$ is to be stated.

Concept introduction:

In metric system of units, the bigger and the smaller units of any quantity are in relation with each other by the factor of $10$. It is the most useful unit system. It is a decimal system of units. For example, if the unit of length is $1\text{kilometer}$ then it is equal to $1000\text{meters}$, according to the metric units.

Answer to Problem 1.100E

The metric system conversion of the given quantity by changing only the power of $10$ is $4.5\times {10}^6\text{mm}$.

Explanation of Solution

The given quantity is $4.5\text{km}$. The conversion of $\text{km}$ into $\text{mm}$ is done as,

$1\text{km}=1\times {10}^6\text{mm}$

Thus, the quantity, $4.5\text{km}$ can be converted into $\text{mm}$ as,

$4.5\text{km}=4.5\times {10}^6\text{mm}$

Therefore, the metric system conversion of the given quantity by changing only the power of $10$ is $4.5\times {10}^6\text{mm}$.

Conclusion

The metric system conversion of the given quantity by changing only the power of $10$ is $4.5\times {10}^6\text{mm}$.

Interpretation Introduction

(b)

Interpretation:

The metric system conversion of the given quantity by changing only the power of $10$ is to be stated.

Concept introduction:

In metric system of units, the bigger and the smaller units of any quantity are in relation with each other by the factor of $10$. It is the most useful unit system. It is a decimal system of units. For example, if the unit of length is $1\text{kilometer}$ then it is equal to $1000\text{meters}$, according to the metric units.

Answer to Problem 1.100E

The metric system conversion of the given quantity by changing only the power of $10$ is $6.0\times {10}^3\text{g}$.

Explanation of Solution

The given quantity is $6.0\times {10}^6\text{mg}$. The conversion of $\text{mg}$ into $\text{g}$ is done as,

$1\text{mg}=1\times {10}^{-3}\text{g}$

Thus, the quantity, $6.0\times {10}^6\text{mg}$ can be converted into $\text{g}$ as,

$\begin{array}{rll}6.0\times {10}^6\text{mg}& =& 6.0\times {10}^6\times {10}^{-3}\text{g}\\ & =& 6.0\times {10}^3\text{g}\end{array}$

Therefore, the metric system conversion of the given quantity by changing only the power of $10$ is $6.0\times {10}^3\text{g}$.

Conclusion

The metric system conversion of the given quantity by changing only the power of $10$ is $6.0\times {10}^3\text{g}$.

Interpretation Introduction

(c)

Interpretation:

The metric system conversion of the given quantity by changing only the power of $10$ is to be stated.

Concept introduction:

In metric system of units, the bigger and the smaller units of any quantity are in relation with each other by the factor of $10$. It is the most useful unit system. It is a decimal system of units. For example, if the unit of length is $1\text{kilometer}$ then it is equal to $1000\text{meters}$, according to the metric units.

Answer to Problem 1.100E

The metric system conversion of the given quantity by changing only the power of $10$ is $9.86\times {10}^{12}\text{km}$.

Explanation of Solution

The given quantity is $9.86\times {10}^{15}\text{m}$. The conversion of $\text{m}$ into $\text{km}$ is done as,

$1\text{m}=1\times {10}^{-3}\text{km}$

Thus, the quantity, $9.86\times {10}^{15}\text{m}$ can be converted into $\text{km}$ as,

$\begin{array}{rll}9.86\times {10}^{15}\text{m}& =& 9.86\times {10}^{15}\times {10}^{-3}\text{km}\\ & =& 9.86\times {10}^{12}\text{km}\end{array}$

Therefore, the metric system conversion of the given quantity by changing only the power of $10$ is $9.86\times {10}^{12}\text{km}$.

Conclusion

The metric system conversion of the given quantity by changing only the power of $10$ is $9.86\times {10}^{12}\text{km}$.

Interpretation Introduction

(d)

Interpretation:

The metric system conversion of the given quantity by changing only the power of $10$ is to be stated.

Concept introduction:

In metric system of units, the bigger and the smaller units of any quantity are in relation with each other by the factor of $10$. It is the most useful unit system. It is a decimal system of units. For example, if the unit of length is $1\text{kilometer}$ then it is equal to $1000\text{meters}$, according to the metric units.

Answer to Problem 1.100E

The metric system conversion of the given quantity by changing only the power of $10$ is $1.91\times {10}^2\text{mg}$.

Explanation of Solution

The given quantity is $1.91\times {10}^{-4}\text{kg}$. The conversion of $\text{kg}$ into $\text{mg}$ is done as,

$1\text{kg}=& 1\times {10}^6\text{mg}$

Thus, the quantity, $1.91\times {10}^{-4}\text{kg}$ can be converted into $\text{mg}$ as,

$\begin{array}{rllll}1.91\times {10}^{-4}\text{kg}& & =& & 1.91\times {10}^{-4}\times {10}^6\text{mg}\\ & & =& & 1.91\times {10}^2\text{mg}\end{array}$

Therefore, the metric system conversion of the given quantity by changing only the power of $10$ is $1.91\times {10}^2\text{mg}$.

Conclusion

The metric system conversion of the given quantity by changing only the power of $10$ is $1.91\times {10}^2\text{mg}$.

Interpretation Introduction

(e)

Interpretation:

The metric system conversion of the given quantity by changing only the power of $10$ is to be stated.

Concept introduction:

In metric system of units, the bigger and the smaller units of any quantity are in relation with each other by the factor of $10$. It is the most useful unit system. It is a decimal system of units. For example, if the unit of length is $1\text{kilometer}$ then it is equal to $1000\text{meters}$, according to the metric units.

Answer to Problem 1.100E

The metric system conversion of the given quantity by changing only the power of $10$ is $5.0\times {10}^{-6}\text{mg}$.

Explanation of Solution

The given quantity is $5.0\text{ng}$. The conversion of $\text{ng}$ into $\text{mg}$ is done as,

$1\text{ng}=& 1\times {10}^{-6}\text{mg}$

Thus, the quantity, $5.0\text{ng}$ can be converted into $\text{mg}$ as,

$5.0\text{ng}=& 5.0\times {10}^{-6}\text{mg}$

Therefore, the metric system conversion of the given quantity by changing only the power of $10$ is $5.0\times {10}^{-6}\text{mg}$.

Conclusion

The metric system conversion of the given quantity by changing only the power of $10$ is $5.0\times {10}^{-6}\text{mg}$.