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Density to v/v% calculations - can you check my work

Hi all,

I have looked at this questions & my working multiple times & not totally confident in my answer, so would appreciate a second pair of eyes to confirm that I haven't lost to plot (or to point out where I have)

Question
An urine sample contains 46 .5 mg L-1 of ethanol. If the density ofethanol is 0.79 g cm-3, express this concentration as a % v/v.
Standard Units
46.5mg/L = 0.0465g/L0.79g/ml = 790g/L
Convert Formula
Density = Mass / Volume (D = M/V)
DV=M
V=M/D

Assumptions (for calculations sake)
Total Volume of Solution = 1000ml

Calculation
Mass of ethanol = 0.0465 g
Volume of ethanol = M/D = 0.0465(g)/790(g/L) = 5.88608 x 10-5Lv/v% = {(5.88608 x 10-5)/1000} x 100% = 5.88608 x 10-6 %

Answer
v/v% = 0.00000589 % (3SF)

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