Question

Need help please!!
A submicroscopic particle suspended in a solution has a volume 1.3um^3. What is this volume in liters?
um = micrometers
1um = (10^-6) m

Answer 1

\[ 1 um =10^{-6} m\]
do you know how many liters are equal to how many meters?

Answer 2

i'm sorry how many CUBIC meters equals how many liters?

Answer 3

\[1 m^3=10^3 L \text{ right ? }\]

Answer 4

\[1 um = 10^{-6 } m \\ \text{ cube both sides } \\ (1 um )^3=(10^{-6} m )^3 \\ 1 um^3=10^{-18} m^3 \]

Answer 5

do you know why I did this?

Answer 6

because we are working with cubic units

Answer 7

\[1.3 um^3 \cdot \frac{10^{-18} m^3}{1 um^3} \text{ this will cancel the } um^3 \text{ units } \]
now we need to get rid of the m^3 units to do that we will also need m^3 on bottom
and we know 1 m^3=10^3 L
\[\text{so we know } \frac{ 10^3 L}{1 m^3 }=1\]

Answer 8

so we will also need to multiply that in

Answer 9

\[1.3 um^3 \cdot \frac{10^{-18} m^3}{1 um^3} \cdot \frac{10 ^3 L}{1 m^3}\]

Answer 10

so all the units will cancel there except the L units on top

Answer 11

which is what we wanted

Answer 12

so now just multiply the numbers on top and and you would divide by the numbers on bottom (but that is just one in this case :))

Answer 13

ok thank you soooo much :)