Chapter 2, Problem 14E

Interpretation Introduction

(a)

Interpretation:

Two unit factors for the given metric relationships are to be stated.

Concept introduction:

The metric system unit is the unit system which is accepted as the standard system of unit internationally. The nonmetric units are the common unit system which is not standard for the parameter to be calculated. The unit factors are calculated by taking the ratio of two equivalent measurement systems.

Answer to Problem 14E

Two unit factors for the given metric relationships are $\frac{1\text{Gm}}{1\times {10}^9\text{m}}$ and $\frac{1\times {10}^9\text{m}}{1\text{Gm}}$.

Explanation of Solution

The giga $\left(\text{G}\right)$ stands for a factor of ${10}^9$. “ $\text{m}$” is the symbol used to denote meter.

The relation showing unit equation between meter $\left(\text{m}\right)$ and giga meters $\left(\text{Gm}\right)$ is given below as,

$1\text{Gm}=1\times {10}^9\text{m}$

The unit factors are calculated by taking the ratio of two equivalent measurement systems. Thus, the unit factor for meter $\left(\text{m}\right)$ and giga meters $\left(\text{Gm}\right)$ can be written as,

$\frac{1\text{Gm}}{1\times {10}^9\text{m}}$

Another unit factor can be written as,

$\frac{1\times {10}^9\text{m}}{1\text{Gm}}$

Conclusion

Two unit factors for the given metric relationships are $\frac{1\text{Gm}}{1\times {10}^9\text{m}}$ and $\frac{1\times {10}^9\text{m}}{1\text{Gm}}$.

Interpretation Introduction

(b)

Interpretation:

Two unit factors for the given metric relationships are to be stated.

Concept introduction:

The metric system unit is the unit system which is accepted as the standard system of unit internationally. The nonmetric units are the common unit system which is not standard for the parameter to be calculated. The unit factors are calculated by taking the ratio of two equivalent measurement systems.

Answer to Problem 14E

Two unit factors for the given metric relationships are $\frac{1\text{Tg}}{1\times {10}^{12}\text{g}}$ and $\frac{1\times {10}^{12}\text{g}}{1\text{Tg}}$.

Explanation of Solution

The tera $\left(\text{T}\right)$ stands for a factor of ${10}^{12}$. “ $\text{g}$” is the symbol used to denote grams.

The relation showing unit equation between grams $\left(\text{g}\right)$ and tera grams $\left(\text{Tg}\right)$ is given below as,

$1\text{Tg}=1\times {10}^{12}\text{g}$

The unit factors are calculated by taking the ratio of two equivalent measurement systems. Thus, the unit factor for grams $\left(\text{g}\right)$ and tera grams $\left(\text{Tg}\right)$ can be written as,

$\frac{1\text{Tg}}{1\times {10}^{12}\text{g}}$

Another unit factor can be written as,

$\frac{1\times {10}^{12}\text{g}}{1\text{Tg}}$

Conclusion

Two unit factors for the given metric relationships are $\frac{1\text{Tg}}{1\times {10}^{12}\text{g}}$ and $\frac{1\times {10}^{12}\text{g}}{1\text{Tg}}$.

Interpretation Introduction

(c)

Interpretation:

Two unit factors for the given metric relationships are to be stated.

Concept introduction:

The metric system unit is the unit system which is accepted as the standard system of unit internationally. The nonmetric units are the common unit system which is not standard for the parameter to be calculated. The unit factors are calculated by taking the ratio of two equivalent measurement systems.

Answer to Problem 14E

Two unit factors for the given metric relationships are $\frac{1\text{dL}}{1\times {10}^{-1}\text{L}}$ and $\frac{1\times {10}^{-1}\text{L}}{1\text{dL}}$.

Explanation of Solution

The deci $\left(\text{d}\right)$ stands for a factor of ${10}^{-1}$. $\text{"L"}$ is the symbol used to denote liters.

The relation showing unit equation between liters $\left(\text{L}\right)$ and deci liters $\left(\text{dL}\right)$ is given below as,

$1\text{dL}=1\times {10}^{-1}\text{L}$

The unit factors are calculated by taking the ratio of two equivalent measurement systems. Thus, the unit factor for liters $\left(\text{L}\right)$ and deci liters $\left(\text{dL}\right)$ can be written as,

$\frac{1\text{dL}}{1\times {10}^{-1}\text{L}}$

Another unit factor can be written as,

$\frac{1\times {10}^{-1}\text{L}}{1\text{dL}}$

Conclusion

Two unit factors for the given metric relationships are $\frac{1\text{dL}}{1\times {10}^{-1}\text{L}}$ and $\frac{1\times {10}^{-1}\text{L}}{1\text{dL}}$.

Interpretation Introduction

(d)

Interpretation:

Two unit factors for the given metric relationships are to be stated.

Concept introduction:

The metric system unit is the unit system which is accepted as the standard system of unit internationally. The nonmetric units are the common unit system which is not standard for the parameter to be calculated. The unit factors are calculated by taking the ratio of two equivalent measurement systems.

Answer to Problem 14E

Two unit factors for the given metric relationships are $\frac{1\text{cs}}{1\times {10}^{-2}\text{s}}$ and $\frac{1\times {10}^{-2}\text{s}}{1\text{cs}}$.

Explanation of Solution

The centi $\left(\text{c}\right)$ stands for a factor of ${10}^{-2}$. “ $\text{s}$” is the symbol used to denote seconds.

The relation showing unit equation between seconds $\left(\text{s}\right)$ and centi seconds $\left(\text{cs}\right)$ is given below as,

$1\text{cs}=1\times {10}^{-2}\text{s}$

The unit factors are calculated by taking the ratio of two equivalent measurement systems. Thus, the unit factor for seconds $\left(\text{s}\right)$ and centi seconds $\left(\text{cs}\right)$ can be written as,

$\frac{1\text{cs}}{1\times {10}^{-2}\text{s}}$

Another unit factor can be written as,

$\frac{1\times {10}^{-2}\text{s}}{1\text{cs}}$

Conclusion

Two unit factors for the given metric relationships are $\frac{1\text{cs}}{1\times {10}^{-2}\text{s}}$ and $\frac{1\times {10}^{-2}\text{s}}{1\text{cs}}$.