Question

Express each of the following in kilograms.

1. $5.84\times {10}^{-3}mg$
2. $58.34g$
3. $0.584g$
4. $5.873\times {10}^{-21}g$

Answer 1

Step $\mathbf{1}$: Convert $\mathbf{5}\mathbf{.}\mathbf{84}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathit{m}\mathit{g}$ into kilogram.

We know that

$1kg=1000,000mg$

That is

$5.84\times {10}^{-3}mg=\frac{5.84\times {10}^{-3}}{{10}^6}kg$

$=5.84\times {10}^{-9}kg$

Step $\mathbf{2}$: Convert $\mathbf{58}\mathbf{.}\mathbf{34}\mathbf{}\mathit{g}$ into kilogram.

We know that

$1kg=1000g$

That is

$58.34g=\frac{58.34}{{10}^3}kg$

$=58.34\times {10}^{-3}kg$

Step $\mathbf{3}$: Convert $\mathbf{0}\mathbf{.}\mathbf{584}\mathbf{}\mathit{g}$ into kilogram.

$0.584g=\frac{0.584}{1000}kg$

$=0.584\times {10}^{-3}kg$

Step $\mathbf{4}$: Convert $\mathbf{5}\mathbf{.}\mathbf{873}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{21}}\mathbf{}\mathit{g}$ into kilogram.

$5.873\times {10}^{-21}g=\frac{5.873\times {10}^{-21}}{{10}^3}kg$

$=5.873\times {10}^{-24}kg$

Hence the required values are

1. $\mathbf{5}\mathbf{.}\mathbf{84}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{}\mathit{k}\mathit{g}$
2. $\mathbf{58}\mathbf{.}\mathbf{34}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathit{k}\mathit{g}$
3. $\mathbf{0}\mathbf{.}\mathbf{584}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathit{k}\mathit{g}$
4. $\mathbf{5}\mathbf{.}\mathbf{873}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{24}}\mathbf{}\mathit{k}\mathit{g}$