Question

How do you convert \[2.21 \times {10^{ - 4}}\] dl into microliters?

Answer 1

Hint: In this question we have to find the convert to dl (deciliter) into microliters of the given number. Next, we use unit conversion. Next, we take the one liter equal to microliters. And also we are going to multiplication and divide in complete step by step solutions.
Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding

Complete step-by-step solution:
To find the change deciliter into microliters of the given number:
Given, \[2.21 \times {10^{ - 4}}\]dl
Here, you can use liters as a base for this conversion.
First, you know that you have two conversion factors here
\[1{\text{ }}L = 10{\text{ }}dL\]and \[1{\text{ }}L = {10^6}\mu L\]
This means that you can convert the volume from deciliters to liters first, then from liters to microliters.
Now, multiply the terms \[\dfrac{{1L}}{{10dL}}\] and \[\dfrac{{{{10}^6}\mu L}}{{1L}}\]in the given number and we get
\[ \Rightarrow 2.21 \times {10^{ - 4}}d{L} \times \dfrac{{1{L}}}{{10d{L}}} \times \dfrac{{{{10}^6}\mu L}}{{1{L}}}\]
\[ \Rightarrow 2.21 \times \left( {{{10}^{ - 4}} \times {{10}^{ - 1}} \times {{10}^6}} \right)\mu L\]
Next, adding and subtraction the 10th powers and we get
 \[ \Rightarrow 2.21 \times \left( {{{10}^{ - 5}} \times {{10}^6}} \right)\mu L\]
\[ \Rightarrow 2.21 \times {10^{ 1}}\mu L\]

\[2.21 \times {10^{ 1}}\mu L\] is the required answer.

Note: We remember that a unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length. Often measurements are given in one set of units, such as feet, but are needed in different units, such as chains. A conversion factor is a numeric expression that enables feet to be changed to chains as an equal exchange.
There is another little hard way to find the answer.
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.
\[ \Rightarrow 1{\text{ }}L = 10{\text{ }}dL\]
\[ \Rightarrow 1{\text{ }}L = {10^6}\mu L\]
Therefore, you know that
\[ \Rightarrow 1{\text{ }}dL = \dfrac{{{{10}^{{{{6}}^5}}}\mu L}}{{1{0}\mu L}}\]
On cancelling the term and we get
\[ \Rightarrow 1{\text{ }}dL = {10^5}\mu L\]
The conversion will now look like this
\[ \Rightarrow 2.21 \times {10^{ - 4}}d{L} \times \dfrac{{{{10}^5}\mu L}}{{1d{L}}}\]
Let us simplify we get
\[ \Rightarrow 2.21 \times {10^{ - 4}} \times {10^5}\mu L\]
On rewriting we get
\[ \Rightarrow 2.21 \times {10^{ 1}}\mu L\]
This is the required answer of the given number.