# Why are numbers used in chemistry often expressed in scientific notation?

May 21, 2017

To reveal honest uncertainty in experimental measurements and ease of reading for very large and very small numbers.

#### Explanation:

There are two reasons to use scientific notation in chemistry. The first is to reveal honest uncertainty in experimental measurements. The second is to express very large or very small numbers so they are easier to read.

HONESTY
Suppose you are trying produce 30 L of some chemical, which you can only make at 10 L a time. Due to tiny imperfections in the measuring equipment, differences in lighting, perception, evaporation, unintended reactions, motion, etc., each batch is measured slightly differently. There is, in effect, some degree of uncertainty to the exact measurements. Here are your measurements:

• $9.998$ L
• $10.01$ L
• $9.8$ L

If you add them all up, you get $29.808$ L. However, giving this answer to your customer is misleading. You were not equally certain of all your measurements. In fact, the measurement with the lowest amount of certainty was the $9.8$ measurement. This is why you use the addition rule of significant figures and say the final result is $29.8$ L.

One of the best ways to reduce ambiguity in numbers with ambiguous significant figures is to write them in scientific notation.

LARGE & SMALL NUMBERS
In scientific inquiry, sometimes you have to deal with very large numbers. For example, the distance from earth to the Milky Way galaxy is about

1,135,300,000,000,000,00000,000 meters

How many zeros is that? How many significant figures is this? This is easier to express in scientific notation, which answers all of these questions right away: $1.1353 \times {10}^{21}$.

Similarly, scientists have the same problem with very small numbers. For example, the diameter of white blood cell is about

0.000012 meters

That is an ugly number! Scientific notation comes to save the day by expressing the same as $1.2 \times {10}^{-} 5$ meters.