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

Oct 8, 2015

$2.21 \cdot {10}^{- 1} \mu \text{L}$

#### Explanation:

You can use liters as a base for this conversion.

You know that you have two conversion factors here

$\text{1 L" = "10 dL }$ and $\text{ 1 L" = 10^6mu"L}$

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

$\text{1 dL" = 10^6/10mu"L" = 10^5mu"L}$

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")