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Answer :
We will solve each conversion step-by-step.
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(a) Convert microliters to [tex]$\mathbf{mm^3}$[/tex]
A microliter is defined as:
[tex]$$1\,\mu L = 10^{-6}\,L.$$[/tex]
Likewise, one cubic millimeter is:
[tex]$$1\,mm^3 = 10^{-6}\,L.$$[/tex]
Since they are both equivalent to [tex]$10^{-6}\,L$[/tex], we have:
[tex]$$1\,\mu L = 1\,mm^3.$$[/tex]
–––––––
(b) Convert [tex]$4.5 \times 10^3\,kg/m^3$[/tex] to [tex]$\mathbf{g/cm^3}$[/tex]
Recall that:
[tex]$$1\,kg = 1000\,g,$$[/tex]
[tex]$$1\,m^3 = 100^3\,cm^3 = 1\,000\,000\,cm^3.$$[/tex]
Thus, the conversion factor is:
[tex]$$1\,\frac{kg}{m^3} = \frac{1000\,g}{1\,000\,000\,cm^3} = 0.001\,\frac{g}{cm^3}.$$[/tex]
Then,
[tex]$$4.5\times10^3\,\frac{kg}{m^3} = 4.5\times10^3 \times 0.001\,\frac{g}{cm^3} = 4.5\,\frac{g}{cm^3}.$$[/tex]
–––––––
(c) Convert [tex]$40.0\,\mu L$[/tex] to [tex]$\mathbf{L}$[/tex]
Since:
[tex]$$1\,\mu L = 10^{-6}\,L,$$[/tex]
we multiply:
[tex]$$40.0\,\mu L = 40.0 \times 10^{-6}\,L = 4.0 \times 10^{-5}\,L.$$[/tex]
–––––––
(d) Convert [tex]$400.00\,dL$[/tex] to [tex]$\mathbf{L}$[/tex]
A deciliter is:
[tex]$$1\,dL = 0.1\,L.$$[/tex]
Thus,
[tex]$$400.00\,dL = 400.00 \times 0.1\,L = 40.0\,L.$$[/tex]
–––––––
(e) Convert [tex]$0.04\,mL$[/tex] to [tex]$\mathbf{GL}$[/tex]
First, convert milliliters to liters:
[tex]$$1\,mL = 10^{-3}\,L,$$[/tex]
so:
[tex]$$0.04\,mL = 0.04 \times 10^{-3}\,L = 4.0 \times 10^{-5}\,L.$$[/tex]
Next, recall that a gigaliter (GL) is:
[tex]$$1\,GL = 10^9\,L.$$[/tex]
Alternatively, we have:
[tex]$$1\,L = 10^{-9}\,GL.$$[/tex]
Thus,
[tex]$$4.0 \times 10^{-5}\,L = 4.0 \times 10^{-5} \times 10^{-9}\,GL = 4.0 \times 10^{-14}\,GL.$$[/tex]
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Final Answers:
- (a) [tex]$1\,\mu L = 1\,mm^3$[/tex]
- (b) [tex]$4.5 \times 10^3\,kg/m^3 = 4.5\,g/cm^3$[/tex]
- (c) [tex]$40.0\,\mu L = 4.0 \times 10^{-5}\,L$[/tex]
- (d) [tex]$400.00\,dL = 40.0\,L$[/tex]
- (e) [tex]$0.04\,mL = 4.0 \times 10^{-14}\,GL$[/tex]
–––––––
(a) Convert microliters to [tex]$\mathbf{mm^3}$[/tex]
A microliter is defined as:
[tex]$$1\,\mu L = 10^{-6}\,L.$$[/tex]
Likewise, one cubic millimeter is:
[tex]$$1\,mm^3 = 10^{-6}\,L.$$[/tex]
Since they are both equivalent to [tex]$10^{-6}\,L$[/tex], we have:
[tex]$$1\,\mu L = 1\,mm^3.$$[/tex]
–––––––
(b) Convert [tex]$4.5 \times 10^3\,kg/m^3$[/tex] to [tex]$\mathbf{g/cm^3}$[/tex]
Recall that:
[tex]$$1\,kg = 1000\,g,$$[/tex]
[tex]$$1\,m^3 = 100^3\,cm^3 = 1\,000\,000\,cm^3.$$[/tex]
Thus, the conversion factor is:
[tex]$$1\,\frac{kg}{m^3} = \frac{1000\,g}{1\,000\,000\,cm^3} = 0.001\,\frac{g}{cm^3}.$$[/tex]
Then,
[tex]$$4.5\times10^3\,\frac{kg}{m^3} = 4.5\times10^3 \times 0.001\,\frac{g}{cm^3} = 4.5\,\frac{g}{cm^3}.$$[/tex]
–––––––
(c) Convert [tex]$40.0\,\mu L$[/tex] to [tex]$\mathbf{L}$[/tex]
Since:
[tex]$$1\,\mu L = 10^{-6}\,L,$$[/tex]
we multiply:
[tex]$$40.0\,\mu L = 40.0 \times 10^{-6}\,L = 4.0 \times 10^{-5}\,L.$$[/tex]
–––––––
(d) Convert [tex]$400.00\,dL$[/tex] to [tex]$\mathbf{L}$[/tex]
A deciliter is:
[tex]$$1\,dL = 0.1\,L.$$[/tex]
Thus,
[tex]$$400.00\,dL = 400.00 \times 0.1\,L = 40.0\,L.$$[/tex]
–––––––
(e) Convert [tex]$0.04\,mL$[/tex] to [tex]$\mathbf{GL}$[/tex]
First, convert milliliters to liters:
[tex]$$1\,mL = 10^{-3}\,L,$$[/tex]
so:
[tex]$$0.04\,mL = 0.04 \times 10^{-3}\,L = 4.0 \times 10^{-5}\,L.$$[/tex]
Next, recall that a gigaliter (GL) is:
[tex]$$1\,GL = 10^9\,L.$$[/tex]
Alternatively, we have:
[tex]$$1\,L = 10^{-9}\,GL.$$[/tex]
Thus,
[tex]$$4.0 \times 10^{-5}\,L = 4.0 \times 10^{-5} \times 10^{-9}\,GL = 4.0 \times 10^{-14}\,GL.$$[/tex]
–––––––
Final Answers:
- (a) [tex]$1\,\mu L = 1\,mm^3$[/tex]
- (b) [tex]$4.5 \times 10^3\,kg/m^3 = 4.5\,g/cm^3$[/tex]
- (c) [tex]$40.0\,\mu L = 4.0 \times 10^{-5}\,L$[/tex]
- (d) [tex]$400.00\,dL = 40.0\,L$[/tex]
- (e) [tex]$0.04\,mL = 4.0 \times 10^{-14}\,GL$[/tex]
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