Question

Perform each of the following conversions using metric conversion factors:

a. $4.82\times {10}^{-5}$L to picoliters

b. $575.2$dm to kilometers

c. $5\times {10}^{-4}$kg to micrograms

d. localid="1651727903680" $6.4\times {10}^{10}$ps to seconds

Short answer

a.$4.82\times {10}^7\mathrm{pL}$

b.$0.0572\mathrm{Km}$

c.$500\mathrm{mg}$

d. $6.4\times {10}^{-2}s$$6.4\times {10}^{-2}\mathrm{s}$

Step-by-step solution

Given Information

Unit conversion for L to pL

Part (a) Explanation

The unit conversion of L into pL can be given as:

$1\mathrm{L}={10}^{12}\mathrm{pL}$

So, $4.82\times {10}^{-5}\mathrm{L}$will be

$4.82\times {10}^{-5}L=4.82\times {10}^{-5}\times {10}^{12}=4.82\times {10}^{7}pL$

Part (b) Given Information

Unit conversion of dm into Km

Part (b) Explanation

The unit conversion for dm into Km can be given as:

So, 575.2 dm will be

$575.5\mathrm{dm}=575.2\times 0.1=0.0572\mathrm{Km}$

Part (c) Given Information

Unit conversion of Kg into mg

Part (c) Explanation

The unit conversion of Kg into mg can be given as:

$1Kg={10}^{6}mg$

So, $5\times {10}^{-4}Kg$will be

$$\begin{gathered} 5\times {10}^{-4}Kg=5\times {10}^{-4}\times {10}^6=5\times {10}^{2}mg \\ or \\ 500mg \end{gathered}$$

Part (d) Given Information

Unit conversion of ps into s

Part (d) Explanation

The unit conversion of picoseconds into seconds can be given as:

$1ps={10}^{-12}s$

So,$6.4\times {10}^{10}ps=6.4\times {10}^{10}\times {10}^{-12}=6.4\times {10}^{-2}s$