Chapter MH, Problem 16PP

Solution

a)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $400\text{cm}$ .

Given information :

The given value is $4\text{m}$ .

It is known that $\text{1}\text{m}\text{=}{\text{10}}^2\text{cm}$ .

Explanation:

The desired conversion is $\text{m}\to \text{cm}$ .

The conversion of the units is given as:

  $\begin{array}{c}4\text{m}=4\cancel{\text{m}}\times \frac{{10}^2\text{cm}}{1\cancel{\text{m}}}\left(\because \text{1}\text{m}\text{=}{\text{10}}^2\text{cm}\right)\\ =400\text{cm}\end{array}$

b)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where a measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $0.5\text{m}$ .

Given information :

The given value is $50.0\text{cm}$ .

It is known that $\text{1}\text{m}\text{=}{\text{10}}^2\text{cm}$ .

Explanation:

The desired conversion is $\text{cm}\to \text{m}$ .

The conversion of the units is given as:

  $\begin{array}{c}50.0\text{cm}=50.0\cancel{\text{cm}}\times \frac{{10}^{-2}\text{m}}{1\cancel{\text{cm}}}\left(\because \text{1}\text{m}\text{=}{\text{10}}^2\text{cm}\right)\\ =0.5\text{m}\end{array}$

c)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where a measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $150\text{mm}$ .

Given information :

The given value is $\text{15}\text{cm}$ .

It is known that $\text{1}\text{cm}\text{=}\text{10}\text{mm}$ .

Explanation:

The desired conversion is $\text{cm}\to \text{mm}$ .

The conversion of the units is given as:

  $\begin{array}{c}\text{15}\text{cm}=15\cancel{\text{cm}}\times \frac{10\text{mm}}{1\cancel{\text{cm}}}\left(\because \text{1}\text{cm}\text{=}\text{10}\text{mm}\right)\\ =150\text{mm}\end{array}$

d)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where a measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $0.567\text{g}$ .

Given information :

The given value is $567\text{mg}$ .

It is known that $\text{1}\text{g}\text{=}{\text{10}}^3\text{mg}$ .

Explanation:

The desired conversion is $\text{mg}\to \text{g}$ .

The conversion of the units is given as:

  $\begin{array}{c}567\text{mg}=567\cancel{\text{mg}}\times \frac{{10}^{-3}\text{g}}{1\cancel{\text{mg}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^3\text{mg}\right)\\ =5.67\times {10}^2\times {10}^{-3}\text{g}\\ \text{= 0}\text{.567}\text{g}\end{array}$

e)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where a measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $0.324\text{L}$ .

Given information :

The given value is $324\text{mL}$ .

It is known that $\text{1}\text{L}\text{=}{\text{10}}^3\text{mL}$ .

Explanation:

The desired conversion is $\text{mL}\to \text{L}$ .

The conversion of the units is given as:

  $\begin{array}{c}324\text{mL}=324\cancel{\text{mL}}\times \frac{{10}^{-3}\text{L}}{1\cancel{\text{mL}}}\left(\because \text{1}\text{L}\text{=}{\text{10}}^3\text{mL}\right)\\ =3.24\times {10}^2\times {10}^{-3}\text{L}\\ \text{=}\text{0}\text{.324}\text{L}\end{array}$

f)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where a measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $28\times {10}^3\text{mL}$ .

Given information :

The given value is $28\text{L}$ .

It is known that $\text{1}\text{L}\text{=}{\text{10}}^3\text{mL}$ .

Explanation:

The desired conversion is $\text{L}\to \text{mL}$ .

The conversion of the units is given as:

  $\begin{array}{c}28\text{L}=28\cancel{\text{L}}\times \frac{{10}^3\text{mL}}{1\cancel{\text{L}}}\left(\because \text{1}\text{L}\text{=}{\text{10}}^3\text{mL}\right)\\ =28\times {10}^3\text{mL}\end{array}$

g)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where a measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $4.6\times {10}^6\text{mm}$ .

Given information :

The given value is $4.6\times {10}^3\text{m}$ .

It is known that $\text{1}\text{m}\text{=}{\text{10}}^3\text{mm}$ .

Explanation:

The desired conversion is $\text{m}\to \text{mm}$ .

The conversion of the units is given as:

  $\begin{array}{c}4.6\times {10}^3\text{m}=4.6\times {10}^3\cancel{\text{m}}\times \frac{{10}^3\text{mm}}{1\cancel{\text{m}}}\left(\because \text{1}\text{m}\text{=}{\text{10}}^3\text{mm}\right)\\ =4.6\times {10}^6\text{mm}\end{array}$

h)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $83\text{kg}$ .

Given information :

The given value is $8.3\times {10}^4\text{g}$ .

It is known that $\text{1}\text{kg}\text{=}{\text{10}}^3\text{g}$ .

Explanation:

The desired conversion is $\text{g}\to \text{kg}$ .

The conversion of the units is given as

  $\begin{array}{c}8.3\times {10}^4\text{g}=8.3\times {10}^4\cancel{\text{g}}\times \frac{{10}^{-3}\text{kg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{kg}\text{=}{\text{10}}^3\text{g}\right)\\ =8.3\times {10}^1\text{kg}\\ \text{=}\text{83}\text{kg}\end{array}$

i)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $2.7\times {10}^5\text{mL}$ .

Given information :

The given value is $2.7\times {10}^2\text{L}$ .

It is known that $\text{1}\text{L}\text{=}{\text{10}}^3\text{mL}$ .

Explanation:

The desired conversion is $\text{L}\to \text{mL}$ .

The conversion of the units is given as:

  $\begin{array}{c}2.7\times {10}^2\text{L}=2.7\times {10}^2\cancel{\text{L}}\times \frac{{10}^3\text{mL}}{1\cancel{\text{L}}}\left(\because \text{1}\text{L}\text{=}{\text{10}}^3\text{mL}\right)\\ =2.7\times {10}^5\text{mL}\end{array}$

j)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $7.3\times {10}^2\text{L}$ .

Given information :

The given value is $7.3\times {10}^5\text{mL}$ .

It is known that $\text{1}\text{L}\text{=}{\text{10}}^3\text{mL}$ .

Explanation:

The desired conversion is $\text{mL}\to \text{L}$ .

The conversion of the units is given as:

  $\begin{array}{c}7.3\times {10}^5\text{mL}=7.3\times {10}^5\cancel{\text{mL}}\times \frac{{10}^{-3}\text{L}}{1\cancel{\text{mL}}}\left(\because \text{1}\text{L}\text{=}{\text{10}}^3\text{mL}\right)\\ =7.3\times {10}^2\text{L}\end{array}$

k)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $8.4\times {10}^7\text{km}$ .

Given information :

The given value is $8.4\times {10}^{10}\text{m}$ .

It is known that $\text{1}\text{km}\text{=}{\text{10}}^3\text{m}$ .

Explanation:

The desired conversion is $\text{m}\to \text{km}$ .

The conversion of the units is given as

  $\begin{array}{c}8.4\times {10}^{10}\text{m}=8.4\times {10}^{10}\cancel{\text{m}}\times \frac{{10}^{-3}\text{km}}{1\cancel{\text{m}}}\left(\because \text{1}\text{km}\text{=}{\text{10}}^3\text{m}\right)\\ =8.4\times {10}^7\text{km}\end{array}$

l)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where a measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $3.8\times {10}^{10}{\text{mm}}^2$ .

Given information :

The given value is $3.8\times {10}^4{\text{m}}^2$ .

It is known that $\text{1}{\text{m}}^2\text{=}{\text{10}}^6{\text{mm}}^2$ .

Explanation:

The desired conversion is ${\text{m}}^2\to {\text{mm}}^2$ .

The conversion of the units is given as

  $\begin{array}{c}3.8\times {10}^4{\text{m}}^2=3.8\times {10}^4\cancel{{\text{m}}^2}\times \frac{{10}^6{\text{mm}}^2}{1\cancel{{\text{m}}^2}}\left(\because \text{1}{\text{m}}^2\text{=}{\text{10}}^6{\text{mm}}^2\right)\\ =3.8\times {10}^{10}{\text{mm}}^2\end{array}$

m)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $6.9\times {10}^8{\text{m}}^2$ .

Given information :

The given value is $6.9\times {10}^{12}{\text{cm}}^2$ .

It is known that $\text{1}{\text{m}}^2\text{=}{\text{10}}^4{\text{cm}}^2$ .

Explanation:

The desired conversion is ${\text{cm}}^2\to {\text{m}}^2$ .

The conversion of the units is given as:

  $\begin{array}{c}6.9\times {10}^{12}{\text{cm}}^2=6.9\times {10}^{12}\cancel{{\text{cm}}^2}\times \frac{{10}^{-4}{\text{m}}^2}{1\cancel{{\text{cm}}^2}}\left(\because \text{1}{\text{m}}^2\text{=}{\text{10}}^4{\text{cm}}^2\right)\\ =6.9\times {10}^8{\text{m}}^2\end{array}$

n)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $6.3{\text{cm}}^3$ .

Given information :

The given value is $6.3\times {10}^{21}{\text{nm}}^3$ .

It is known that $\text{1}{\text{cm}}^3\text{=}{\text{10}}^{21}{\text{nm}}^3$ .

Explanation:

The desired conversion is ${\text{nm}}^3\to {\text{cm}}^3$ .

The conversion of the units is given as:

  $\begin{array}{c}6.3\times {10}^{21}{\text{nm}}^3=6.3\times {10}^{21}\cancel{{\text{nm}}^3}\times \frac{{10}^{-21}{\text{cm}}^3}{1\cancel{{\text{nm}}^3}}\left(\because \text{1}{\text{cm}}^3\text{=}{\text{10}}^{21}{\text{nm}}^3\right)\\ =6.3{\text{cm}}^3\end{array}$

o)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $9.4\times {10}^6{\text{m}}^3$ .

Given information :

The given value is $9.4\times {10}^{12}{\text{cm}}^3$ .

It is known that $\text{1}{\text{m}}^3\text{=}{\text{10}}^6{\text{cm}}^3$ .

Explanation:

The desired conversion is ${\text{m}}^3\to {\text{cm}}^3$ .

The conversion of the units is given as:

  $\begin{array}{c}9.4\times {10}^{12}{\text{cm}}^3=9.4\times {10}^{12}\cancel{{\text{cm}}^3}\times \frac{{10}^{-6}{\text{m}}^3}{1\cancel{{\text{cm}}^3}}\left(\because \text{1}{\text{m}}^3\text{=}{\text{10}}^6{\text{cm}}^3\right)\\ =9.4\times {10}^6{\text{m}}^3\end{array}$

p)

Interpretation : The measurements as indicated are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The converted measurement is $5.7\times {10}^5{\text{km}}^3$ .

Given information :

The given value is $5.7\times {10}^{20}{\text{cm}}^3$ .

It is known that $\text{1}{\text{km}}^3\text{=}{\text{10}}^{15}{\text{cm}}^3$ .

Explanation:

The desired conversion is ${\text{cm}}^3\to {\text{km}}^3$ .

The conversion of the units is given as:

  $\begin{array}{c}5.7\times {10}^{20}{\text{cm}}^3=5.7\times {10}^{20}\cancel{{\text{cm}}^3}\times \frac{{10}^{-15}{\text{km}}^3}{1\cancel{{\text{cm}}^3}}\left(\because \text{1}{\text{km}}^3\text{=}{\text{10}}^{15}{\text{cm}}^3\right)\\ =5.7\times {10}^5{\text{km}}^3\end{array}$