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## Numbers & Operations - The Real & Complex Number Systems 176-188

### Course: Numbers & Operations - The Real & Complex Number Systems 176-188 > Unit 1

Lesson 4: Comparing 2 & 3-digit numbers# Greater than and less than symbols

This video teaches comparing numbers using equal, greater than, and less than symbols. It clarifies the equal sign's meaning and demonstrates using comparison symbols with numbers and expressions. Created by Sal Khan.

## Want to join the conversation?

- how can u always remember what sign means what? I always forget :((((0 votes)
- Here's a trick that's sometimes used. Think of the inequality as a hungry alligator. He always wants to eat the larger number.

4 < 10: The alligator is eating the 10. So, the is 4 is less than 10.

10 > 4: This is 10 is greater than 4

Hope this helps.(6 votes)

- thanks but how do we rate decimals least to greatest?(27 votes)
- You always start from the number that is the farthest left and then continue to the right until one number is different.

Example:

Arrange these numbers from least to greatest:

23.476, 19.894, 23.451

So start with the number that is farthest left. In this case that number is in the tens column.

23.476 has 2 tens, 19.894 has 1 ten, and 23.451 has 2 tens.

This means that 19.894 is smaller than the other numbers.

Now you move on to the ones column for the remaining numbers.

23.476 has 3 ones and 23.451 has 3 ones.

Since they both have an equal amount of ones you need to go further.

Now we look at the first decimal place.

23.476 has 4 tenths and 23.451 has 4 tenths.

Since they both have an equal amount of tenths you need to continue.

Now we look at the second decimal place.

23.476 has 7 hundredths and 23.451 has 5 hundredths.

This means that 23.451 is smaller than 23.476.

So the answer from least to greatest is:

19.894, 23.451, 23.476(30 votes)

- What is quantity?(11 votes)
- "Quantity" can refer simply to the number of items, or it might be some other value. It is not necessarily the "number" of things, but might instead refer to an
**amount**.

For example, if you were asked to measure out a quantity of corn, you would not (unless you were very silly and had a lot of time on your hands!) count out individual grains of corn. Instead, your quantity would probably be measured in terms of mass (eg. 25 kg) or volume (eg. 1 cubic metre).

Counting grains is**possible**but impractical.

In other instances, counting individual particles might be virtually impossible (eg. measuring sand) or wholly impossible, such as when measuring a liquid.(2 votes)

- For remembering the which sign means greater than and which sign mean less than, couldn't we remember it in way that that can make it more meaningful? When I was learning this before this site even existed, we learned that the greater than and less than sigh is like the smaller eating the larger. That how people like me learned it.(6 votes)
- The alligator always want to eat the bigger number. So the opening should face toward the bigger number.(5 votes)

- how do u compare =numbers(6 votes)
- You don't really compare = numbers since 5 isn't bigger than 5 or less than 5. Two equal numbers aren't bigger or smaller than themselves, they are equal

Hope this helps!(0 votes)

- Does a number that is both equal and greater than exist? (Sorry if that's confusing)(2 votes)
- When you have the greater than symbol with the equal, it means "greater than OR equal to".

Examples:

5 >= 2 would be true as 5 is larger than 2

2 >= 2 would be true as 2 = 2

0 >= 2 would be false as 0 is neither greater than 2 nor is it equal to 2.

Hope this help.s(6 votes)

- Why didn't you go into greater/less than or equal to symbols? What are those even for?(3 votes)
- He might have not included that because it is in a later lesson. The greater and less symbols are the algebraic symbols to show greater and less numbers.(3 votes)

- What does the simbol with the line mean?(2 votes)
- ≠ means not equal, that there is a difference between what you are comparing(4 votes)

- I know that there are imaginary numbers too. But how do you compare imaginary numbers with real numbers, like 4 and 3i?(2 votes)
- Because imaginary numbers are, as you say, imaginary, there is no way of comparing them to real numbers. We cannot plot them on a real number line or a real graph.(3 votes)

- ≥ What if the sign looks like this.(2 votes)
- This is an "or equal to" sign it's the same as the Greater than symbol with an equality sign under neath. Is 10 ≥ 9 it would be > than 9. If 10 ≥ 10 it would be 10 = 10.(2 votes)

## Video transcript

Most of us are familiar with
the equal sign from our earliest days of arithmetic. You might see something
like 1 plus 1 is equal to 2. Now, a lot of people might
think when they see something like this that somehow equal
means give me the answer. 1 plus 1 is the problem. Equal means give me the
answer and 1 plus 1 is 2. That's not what
equal actually means. Equal is actually just trying
to compare two quantities. When I write 1 plus 1
equals 2, that literally means that what I
have on the left hand side of the equal sign is the
exact same quantity as what I have on the right hand
side of the equal sign. I could have just as easily have
written 2 is equal to 1 plus 1. These two things are equal. I could have written
2 is equal to 2. This is a completely
true statement. These two things are equal. I could have written 1 plus
1 is equal to 1 plus 1. I could have written 1 plus 1
minus 1 is equal to 3 minus 2. These are both equal quantities. What I have here on
the left hand side, this is 1 plus 1 minus 1 is 1
and this right over here is 1. These are both equal quantities. Now I will introduce
you to other ways of comparing numbers. The equal sign is when I
have the exact same quantity on both sides. Now we'll think
about what we can do when we have different
quantities on both sides. So let's say I have the number
3 and I have the number 1 and I want to compare them. So clearly 3 and
1 are not equal. In fact, I could
make that statement with a not equal sign. So I could say 3
does not equal 1. But let's say I want to figure
out which one is a larger and which one is smaller. So if I want to have some
symbol where I can compare them, where I can tell, where I can
state which of these is larger. And the symbol for doing that
is the greater than symbol. This literally would be
read as 3 is greater than 1. 3 is a larger quantity. And if you have trouble
remembering what this means-- greater than-- the larger
quantity is on the opening. I guess if you could view
this as some type of an arrow, or some type of symbol, but
this is the bigger side. Here, you have this
little teeny, tiny point and here you have the big
side, so the larger quantity is on the big side. This would literally
be read as 3 is greater than--
so let me write that down-- greater than,
3 is greater than 1. And once again, it just doesn't
have to be numbers like this. I could write an expression. I could write 1 plus 1 plus 1 is
greater than, let's say, well, just one 1 right over there. This is making a comparison. But what if we had things
the other way around. What if I wanted to make
a comparison between 5 and, let's say, 19. So now the greater than
symbol wouldn't apply. It's not true that 5
is greater than 19. I could say that 5
is not equal to 19. So I could still
make this statement. But what if I wanted to make
a statement about which one is larger and which
one is smaller? Well, as in plain
English, I would want to say 5 is less than 19. So I would want to say--
let me write that down-- I want to write 5 is less than 19. That's what I want to say. And so we just have to think
of a mathematical notation for writing "is less than." Well, if this is
greater than, it makes complete sense that
let's just swap it around. Let's make, once
again, the point point towards the smaller
quantity and the big side of the symbol point to
the larger quantity. So here 5 is a smaller
quantity so I'll make the point point there. And 19 is a larger quantity,
so I'll make it open like this. And so this would be read
as 5 is less than 19. 5 is a smaller quantity than 19. I could also write this
as 1 plus 1 is less than 1 plus 1 plus 1. It's just saying that this
statement, this quantity, 1 plus 1 is less
than 1 plus 1 plus 1.