# How many liters are in 2.10 kiloliter?

Jan 28, 2016

$2.10 \cdot {10}^{3} \text{L}$

#### Explanation:

Before doing any calculations, make sure that you understand what you're looking for here.

The metric system uses prefixes to denote multiples or fractions of basic units. In order to get from a basic unit to a multiple, you multiply by powers of $10$. Likewise, to get from a basic unit to a fraction, you divide by powers of $10$.

In your case, the kilo- prefix is used to denote a multiple if the basic unit, which here is the liter. So, in order to go from liters to kiloliters, you must multiply by ${10}^{3}$.

In essence, this means that you have

$\text{1 kL" = 10^3"L}$

Simply put, you need $\text{1000 L}$ in order to have $\text{1 kL}$.

This means that you will have

2.10 color(red)(cancel(color(black)("kL"))) * (10^3"L")/(1color(red)(cancel(color(black)("kL")))) = "2100 L"

In order to express this number rounded to three sig figs, you need to use scientific notation. The answer will thus be

"2.10 kL" = color(green)(2.10 * 10^3"L")