# Comparing Numbers Written in Scientific Notation

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• 0:01 Scientific Notation
• 1:01 How to Compare Numbers
• 2:07 Which Is Larger?
• 3:08 Which Is Smaller?
• 4:26 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to compare numbers written in scientific notation with each other. You will learn how to tell which is larger and which is smaller.

## Scientific Notation

Imagine that you are a scientist working for the government. Your job is to look through test data from other researchers. Right now you are working on a rather important project. And so, you are looking at a piece of paper with a lot of numbers written in scientific notation, a special way to write numbers. These numbers are written in scientific notation because they are either very large or very small.

Remember that your numbers written in scientific notation all have a multiplication by 10 to a power. So, some of the numbers you are seeing are numbers such as 2.3 * 10^12, 4.67 * 10^54, 3.12 * 10^-9, etc. Your job is to put these numbers in order so that you can better understand the data.

## How to Compare Numbers

What you need to do is to compare these numbers to each other. You need to be able to determine which number is larger and which is smaller. Let me first give you the steps you need to take to do so, and then we will look at a couple of examples.

There are only two steps you need to take. The first is to look at the power and compare these numbers together. If one is larger or smaller, then you already know which number is larger or smaller. The larger the exponent, the larger the number is. And, vice versa, the smaller the exponent, the smaller the number is. If your powers are the same, then you move on to the second step. If they are not the same, then you are done comparing the numbers.

The second step is to look at the number before the multiplication by 10 if the powers are the same. Treat these like you would normal numbers. If one is larger, then that number is larger, and if one is smaller, then that number is smaller. Let's look at a couple of examples now to see how it all works.

## Which Is Larger?

Which is larger? 3.2 * 10^12 or 4.7 * 10^11?

We begin with the first step. We compare the powers. We have a 12 and an 11. Well, the 12 is larger, so that tells us right away that the number 3.2 * 10^12 is the larger number, and we are done.

Now, compare the numbers 3.5 * 10^8 and 6.7 * 10^8 to see which is larger.

The first step is to compare our powers. Both are 8. So, that means we now need to move on to the second step, and compare the numbers in front of our multiplication by 10. We have a 3.5 and a 6.7. Which is larger? The 6.7 is larger, so that means that number is larger. So, our larger number is 6.7 * 10^8.

## Which Is Smaller?

Now, let's look at some examples of figuring out which number is smaller.

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