Question

How many milliliters are in \[36.2dL\]?

Answer 1

Hint: Here, we will use the concept of conversion of units. Both milliliters and deciliters are units of a quantity of a liquid and deciliters are a larger unit than milliliters. We will convert the given quantity from one unit to another unit by multiplying the converting factor to it.

Formula Used:
We will use the following conversion:
1. 1 liter is equal to 10 deciliters i.e., 1 Liter \[ = \] 10 deciliters
2. 1 liter is equal to 1000 milliliters i.e., 1 Liter \[ = \] 1000 milliliters

Complete Step by Step Solution:
We know that 1 liter is equal to 10 deciliters i.e., 1 Liter \[ = \] 10 deciliters
We know that 1 liter is equal to 1000 milliliters i.e., 1 Liter \[ = \] 1000 milliliters
Now, by dividing the conversion units, we get
\[\dfrac{{dL}}{{mL}} = \dfrac{{10}}{{1000}}\]
Now, by cancelling out the factors, we get
\[ \Rightarrow \dfrac{{dL}}{{mL}} = \dfrac{1}{{100}}\]
We are given \[36.2dL\] deciliters. Now, we will find milliliters in the given deciliters, so we get
\[ \Rightarrow \dfrac{{dL}}{{mL}} = \dfrac{{36.2}}{{mL}}\]
Since \[\dfrac{{dL}}{{mL}} = \dfrac{1}{{100}}\], we get
\[ \Rightarrow \dfrac{{36.2}}{{mL}} = \dfrac{1}{{100}}\]
Now, by multiplying the numerator and the denominator, we get
\[ \Rightarrow \dfrac{{36.2}}{{mL}} = \dfrac{1}{{100}} \times \dfrac{{36.2}}{{36.2}}\]
\[ \Rightarrow \dfrac{{36.2}}{{mL}} = \dfrac{{36.2}}{{3620}}\]

Therefore, the milliliters in \[36.2dL\] is \[3620mL\].

Note:
We know that a milliliters is defined as a unit of volume of a liquid representing \[\dfrac{1}{{1000}}\] of a liter. It is denoted by the symbol \[mL\]. A deciliter is defined as a unit of volume of a liquid representing \[\dfrac{1}{{10}}\] of a liter. It is denoted by the symbol \[dL\]. Whenever the conversion is made from the smaller unit into the larger unit, then the common factor has to be divided whereas the conversion is made from the larger unit into the smaller unit, then the common factor has to be multiplied. This is common for all the conversion of SI units. These units should be remembered in finding the ratios and proportion of similar quantities. We can calculate the milliliters in the given deciliters by multiplying the given deciliters with 100.
We know that 1 deciliter is equal to 100 milliliters i.e., 1 deciliter \[ = \] 1 milliliter
\[ \Rightarrow 36.2dL = 36.2 \times 100mL\]
Now, by converting the decimal into a fraction, we get
\[ \Rightarrow 36.2dL = \dfrac{{362}}{{10}} \times 100mL\]
\[ \Rightarrow 36.2dL = 3620mL\]
Therefore, the milliliters in \[36.2dL\] is \[3620mL\].