Relative Magnitude of Numbers: Definition & Examples

Instructor: Yuanxin (Amy) Yang Alcocer

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

Read this lesson to learn how you can go about deciding whether one particular number is greater or lesser than another. Also in this lesson, you'll see how negative numbers seem to go contrary to what you would expect.

Definition

Your friend just offered to trade you negative one million dollars if you give him one dollar. It sounds like a pretty good deal. One million is a really big number. But you feel a little unsure about that word, 'negative.' If only you knew the magnitude of negative one million compared to one.

In math, magnitude is the size of one number compared to another. For instance, is negative one million bigger than one?

Let's take a closer look.

Positive Numbers

Positive numbers are the numbers you count with, like 1, 2, 3, and so on. You can visualize positive numbers using objects in the real world, such as this image of two fries.

2
magnitude

Now, say you are comparing the numbers 2 and 5.

2 and 5
magnitude

Looking at your fries, you can easily see that 5 is larger than 2. In math notation, you can use the greater than symbol to show this: 5 > 2. Notice that the greater than symbol looks like a mouth opening towards the larger number. You can also use the less than symbol to show that 2 is smaller than 5: 2 < 5.

If your two numbers are equal to each other, then you use the equal sign. For example, say you are comparing the numbers 2 and 2.000.

2 and 2
magnitude

When you visualize it, you can clearly see that they are the same amount. In math notation, you would write it with an equal sign like this: 2 = 2.000.

Negative Numbers

When it comes to comparing positive numbers, things make sense because you can visualize them. But, when you being comparing negative numbers, things get a little confusing. Don't simply trust what looks right.

To help you compare the magnitude of your negative numbers, keep a mental image of the negative side of the number line.

The Number Line
magnitude

Notice that negative numbers begin towards the left of the 0 on the number line. On the number line, as you go towards the left, numbers get smaller. When you go towards the right, numbers get larger. That means the higher the negative number, the smaller its relative magnitude.

Just remember, when it comes to negative numbers, larger numbers means smaller magnitude. So, -10 is actually smaller than -5 even though -10 is a bigger number than -5. As you can see on the number line, the -10 is to the left of the -5. You can use the greater than or less than symbols to compare negative numbers, too, such as -10 < -5 or -5 > -10.

By now, you're probably thinking that you shouldn't trade your one dollar for your friends negative one million dollars. That's right. Your dollar has a much higher relative magnitude than his negative one million.

Decimals

It can be a little tricky to compare magnitude in decimals. For example, 3.4 > 3.391 even though 3.391 has more digits than 3.4. The number line is a big help here. Number 3.4 is almost halfway between 3 and 4. But 3.391 is between 3.3 and 3.4. Number 3.391 actually ends up slightly to the left of 3.4. So, it's smaller than 3.4.

3.4 and 3.391
magnitude

Ordering Numbers

Now that you understand relative magnitude, you can put numbers in order.

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