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
6.3005×103
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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Learn More:
- Multiplication with Decimals and Some Examples
- Learn More about Exponents
- Working with Decimals: Addition and Subtraction
- Powers: What They Are and What They Are For
- Multiplying and Dividing Decimal Numbers by Powers of 10
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