The Number 0: What It Is and How to Use It (2024)

The Number 0: What It Is and How to Use It (1)

The number 0 has long stumped people who are learning math concepts. Is zero a number? How do we use it? Though we all know on some level that zero means none or nothing, that doesn’t always help us incorporate it into math problems. Below we will go over a few basic functions of zero and how to solve equations containing zero using those functions.

What Is the Number 0?

Is zero a number? Zero, or 0, is a number and the numerical digit used to represent the number 0 is widely used in mathematics, and can be used as a number in its own right, or as a placeholder in equations.


The number 0 has been around to represent the idea of nothing since ancient Sumerian society, who used it to represent an absence of a number when writing out numbers and equations.

The oval shape we know today as 0 appeared in the Arabic language in the late 700’s. Zero didn’t start appearing in European society until the late 12th century.

Modern Use

Zero is commonly used in language to express the concept of having none, and is used in math as an integer. The number 0 in today’s math can be tricky; why calculate something when there’s not actually anything there? But zero can be used in a variety of math problems, and it’s important to know what to do with zero when you see it.

Operations With 0

While this list of functions using zero doesn’t encompass all functions of math, these basic arithmetic instructions using zero will help you solve problems on tests and maybe even in the real world.


Identity Law of Addition states that any number added to 0 is equal to itself.

Therefore, you can add any number and get the same sum. So you can add 0 to 1, 107, and 1,000,000 and still get the same number that you started with.


Like addition, if you subtract 0 from any number, you get the same sum. For example, 12-0 = 12.

If you’re subtracting, you may need to use borrowing to solve the problem. Borrowing is a method used for subtracting numbers with more than one digit.

Here is an example of borrowing (will figure out how to format):

1572-125 = x

In this problem, you can’t subtract 5 from 2. So, you have to borrow from the 7.

70 is 7 tens. So, you can take a ten away, and the 7 becomes 2; then, the 2 becomes a 12. Now you have to subtract 5 from 12.

12-5 is 7.

6-2 is 4.

5-1 is 4.

1-0 (empty space) is 1.

Therefore, the answer is 1447.

So, if 0 is nothing, how do we borrow from it in a subtraction problem? The key is to borrow from the next digit to the left. You can go as far to the left as you need to.

So if you were to do 306-98 you would first borrow from the 3, to make the 0 a 10. Then, you can borrow from the 10 to make the 6 a 16. So your problem will look like: 16-8=8.



So your answer is 208.

The Number 0: What It Is and How to Use It (2)

Feel free to practice math by adding kittens to your life


Multiplying by 0 is actually one of the easiest functions of 0. When you multiply by 0, the answer is always 0.

12 × 0 = 0

255 × 0 = 0

1679 × 0=0

And guess what? 123596395539 x 0 = 0


The number 0 divided by any number is zero. Think of it like this: division is about dividing, or splitting things evenly, right? If you have a box of 8 cupcakes, and 4 people at your table, you would divide 8 by 4, and discover that everyone gets two cupcakes. But if you have 4 people at your table and a box with 0 cupcakes, you have nothing to actually divide. Everyone gets 0 cupcakes.

Unfortunately, dividing a number by zero is not as obviously logical. Any number divided by zero is considered undefined; if you put it in your calculator right now, you’d probably get an error message.

In division, you can always double check your answer by multiplying the quotient (the answer to the division problem) by the dividend. In our cupcake problem, that’s 2 x 4. The number should equal our original divisor, 8.

However, this serves as a way to help us understand why we cannot divide a number by 0. Since we know from our multiplication rules that anything multiplied by 0 is 0, the concept laid out above doesn’t hold up if 0 is a dividend, because the answer would always be 0, even if that’s not the original divisor.

If for some reason you encountered 0 as a dividend in a problem, you can express it as 1, even though the answer is technically undefined.


Like in division, 0 in exponential is considered undefined. However, when solving problems and you encounter something that is 0 to the power of another number, or a number to the power of 0, remember the 0 exponent rule

The 0 exponent rule says that any base with an exponent of zero or 0 is equal to 1. So x¹ = 1.

Meanwhile, 0 to any power equals 0. So 0² = 0.

The Number 0: What It Is and How to Use It (3)

Zero Factorial

A factorial is a mathematical expression, expressed by ! that equals a number that is found by multiplying numbers all the numbers between 1 and the integer given.

So, 2! means we multiply all the numbers between 1 and 2. That means that 2! = 2×1 = 2 and therefore 2! = 24

6! means that we multiply all the numbers between 1 and 6. So 6! = 1×2×3×4×5×6 = 720 and therefore 6! = 720

A zero factorial, often written as 0! Is defined as equal to 1. Basically, since a factorial is an expression of the product of all the integers between the numbers given and 1, this is the only technically correct answer for 0! because the only number between 0 and 1 is 1.

Using the number zero can be tricky, but there are a few rules that will help you correctly do math when zero is involved. Make sure to stick to these rules, and keep in mind that zero is not your enemy. If you know how to work with the number zero, using it will feel like a piece of cake.

What's Next?

Fascinated by the number zero? Learn how many zeros are in a billion and how many zeros in a googol and a googolplex.

Need more math help? Learn about how to convert decimals to fractions, adding and subtracting fractions, and all about composite and rational numbers. And don't forget our handy multiplication table.

Have friends who also need help with test prep? Share this article!

About the Author

Carrie holds a Bachelors in Writing, Literature, and Publishing from Emerson College, and is currently pursuing an MFA. She worked in book publishing for several years, and believes that books can open up new worlds. She loves reading, the outdoors, and learning about new things.

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The Number 0: What It Is and How to Use It (2024)


The Number 0: What It Is and How to Use It? ›

0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures.

How is the number 0 used? ›

Zero is an important number, even though it represents a quantity of nothing! To summarize: Zero is a number between negative numbers and positive numbers. It is necessary as a placeholder in whole numbers and decimal numbers. It represents a place with no amount or null value.

How do we use the number 0 today? ›

Today the number zero in the numeral system is used to represent the absence of object or quantity. Each student learns the number 0 from primary school, learning it with the number system for counting, mathematically, with negative numbers and whole numbers.

How useful is the number 0? ›

Zero helps us understand and explain concepts that do not have physical forms! The number zero is used as a placeholder in the place value system. For example, two zeros before a number indicate a hundred position, while a single zero before a digit indicates a tens position.

How useful is zero in our life? ›

We deal with zero in all aspects of mathematics and science, and it is important to the function of the world we live in today. From finances, to temperature, to functions, to complex calculus, zero is crucial to the function of our world, despite missing it for years.

Why is zero special? ›

It reflects the concept of zero as representing nothing -- so nothing added to something leaves that something unchanged -- zero is the only number that doesn't alter other numbers through addition or subtraction.

What does the number 0 mean spiritually? ›

As a result, in numerology, zero is often associated with potential and possibilities, and all that comes before the changes. If zeros keep popping up in your life anywhere from receipts to invoices, these appearances may be signaling new opportunities and possibilities.

What is the use of zero today? ›

Modern Use

Zero is commonly used in language to express the concept of having none, and is used in math as an integer.

What is a fun fact about zero? ›

Zero is the only real number that's neither positive nor negative. Zero is the additive identity, that is: a+0=a. We can also prove that zero is the only additive identity: if there were another number x with the same property, that is, a+x=a, we would have: a+0=a=a+x → x=0.

Why is 0 powerful? ›

Zero as a Powerful Placeholder: Beyond its numerical value, zero's significance lies in its role as a placeholder in positional numeral systems. This breakthrough allowed for the representation of numbers with unprecedented efficiency and precision.

What is the story behind zero? ›

The first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.

What does the number zero symbolize? ›

This number symbolizes infinite possibilities and potential, and in that endless supply of opportunities, 0 indicates that you are more than capable of accomplishing things you never thought possible.

What does zero represent? ›

0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures.

How does zero change the world? ›

Without zero, there's no calculus, which means no modern engineering or automation. Without zero, much of our modern world literally falls apart.” The strings of zeros and ones is known as “binary code”, the system on which modern-day computers operate, on the principle of two possible states, “on” and “off”.

What would happen if 0 didn't exist? ›

Having no zero would unleash utter chaos in the world. Maths would be different ball game altogether, with no fractions, no algebra and no calculus. A number line would go from -1 to 1 with nothing bridging the gap. Zero as a placeholder has lots of value and without it a billion would simply be “1”.

Why is 0 the most powerful number? ›

0 definitely. It explodes values to infinity if you divide by it, or makes them disappear if you multiply them by it. Also, rearranging a non-linear equation to equal zero is the first step to solve it.

Where does 0 go in the real number system? ›

0 is a member of the set of integers (a subset of reals). If you start with natural numbers as the basic “self evident” set of discrete quantities, then you add zero to the set of integers by bringing in the operation of subtraction. (Not only that, but some systems of math define 0 is a basic part of the system.)

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