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## What Is Scientific Notation and Why Do We Use It?

What is scientific notation? Why do we use it? How do we use it? How can we write a number in scientific notation? These are some questions that we’ll answer in today’s post.

##### What is scientific notation and why do we use it?

Working with very large or small quantities usually ends up being quite complicated. Scientific notation is a way to write numbers in an abbreviated way, making it easier to work with these numbers.

##### How can you write numbers in scientific notation?

All numbers written in scientific notation are written in two parts:

1. A number that only has a 1s place and decimals.
2. An exponent that indicates the power of 10.

Let’s look at an example to get an idea of how numbers are written in scientific notation: We’re going to try to understand this way of writing numbers:

##### Why do we multiply by a power of 10?

Multiplying by a power of 10 allows us to move the decimal…

• To the right, when the exponent is positive (when we are multiplying by a number greater than or equal to 10). For example:

75×10 = 750

75×100 = 75×10 2 =7500

35.69×10 = 356.9

35.69×100 = 35.69×10 2 = 3569

• To the left, when the exponent is positive (when multiplying by a number less than 1). By doing so, we make the number “smaller”:

75× 10-1= 75/10 = 7.5

75×10-2 = 75/100 = 0.75

35.69×10-1 = 3.569

35.69×10-2 = 35.69/100 = 0.3569

##### Why does the decimal portion only have a 1’s place and decimals?

It only has a 1s place and decimals so that it follows the universal format that is understood everywhere in the world. In addition to being universal, it helps us compare quantities with a single glance as we can focus on the power of 10. The bigger the exponent is, the bigger the number.

##### For example:

Let’s order the following numbers in scientific notation:

3.6352× 10 2

8.235×10-1

6.3005×103

1.3225× 104

Carefully looking at the exponent, we can order the numbers from least to greatest:

8.235×10-1 < 3.6352× 10 2 < 6.3005×103  < 1.3225×104

-1     <      2     <     3      <     4

0.8235   <   363.52   <   6300.5   <   13225

That wraps it up for scientific notation. Can you think of another reason why it’s useful?

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