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:

- A number that only has a 1s place and decimals.
- 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×**10 ^{3}**

1.3225× **10 ^{4}**

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

8.235×**10 ^{-1}** < 3.6352×

**10**< 6.3005×

^{2}**10**

^{3}**< 1.3225×**

**10**

^{4}-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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### Learn More:

- Multiplication with Decimals and Some Examples
- Learn More about Exponents
- Powers: What They Are and What They Are For
- Powers in Math
- Properties of Powers II

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