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QUESTION

# 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")