How do you convert 2.21 x 10 ^-4 dl into microliters?

##2.21 * 10^(-1)mu"L"##

You can use liters as a base for this conversion.

You know that you have two conversion factors here

##"1 L" = "10 dL "## and ##" 1 L" = 10^6mu"L"##

This means that you can convert the volume from deicliters to liters first, then from liters to microliters

##2.21 * 10^(-4)color(red)(cancel(color(black)("dL"))) * (1color(red)(cancel(color(black)("L"))))/(10color(red)(cancel(color(black)("dL")))) * (10^6mu"L")/(1color(red)(cancel(color(black)("L")))) = color(green)(2.21 * 10^(-1)mu"L")##

Alternatively, you can use the two conversion factors to find a single conversion factor that will take you from deciliters to microliters without going through liters.

##{ ("1 L" = "10 dL"), ("1 L" = 10^6mu"L") :} implies "10 dL" = 10^6mu"L"##

Therefore, you know that

##"1 dL" = 10^6/10mu"L" = 10^5mu"L"##

The conversion will now look like this

##2.21 * 10^(-4)color(red)(cancel(color(black)("dL"))) * (10^5mu"L")/(1color(red)(cancel(color(black)("dL")))) = color(green)(2.21 * 10^(-1)mu"L")##