What's the difference between 4 types of numbers (whole, integers, rational, irrational)?

What do hopscotch, temperature, and bank accounts all have in common? They all use types of numbers to express information.

Photo by Volkan Olmez on Unsplash

Why does that matter? ❔❓

We use different types of numbers to express different things. 🔢

Understanding the differences between whole numbers, integers, rational numbers, and irrational numbers will help to express yourself numerically in the real world.

We use numbers to count money, keep track of scores in a sports game, track dates and time, and manage finances. But...

What exactly is a number in math?

"A number is an arithmetic value used for representing the quantity and used in making calculations." In other words, it's a value that shows an amount of something.

Why are there different types of numbers?

Numbers have different properties or characteristics, and are in different places on the number line. Their placement and properties can be put into different categories or groups to help us understand them.

To hear an audio description of the number lines above, click the play button on the audio player below:

What are examples of number types?

• whole numbers

• integers

• rational

• irrational

Whole numbers are the positive numbers 0, 1, 2, 3, 4, 5...and so on, without any decimals or fraction parts.

Examples:

• 3

• 10

• 104

• 3,206

• 1,000,005

Whole numbers in the real world:

• $36 in my bank account💲

• 0º Celsius or 32º Fahrenheit today ❄

• 2 miles from home to school 🚗🏫

Integers are the positive and negative numbers without any decimals or fraction parts. They also include zero.

Examples:

• -100

• 203

• -5

• 30,000

• 0

Integers in the real world:

• -$0.45 in my bank account. Looks like an overdraft! 🙀

• -15º Celsius or 5º Fahrenheit today 🥶

• 25 miles from home to the theater 🚗🎭

Rational numbers can be made by dividing an integer by another integer. They can be written as integers and fractions. They can also be written as terminating (or stopping) decimals and repeating decimals.

Note: If the decimal can be rewritten as a fraction, then the decimal is rational.

MathisFun

🌟 Bonus: You can see the word "ratio" in rational numbers. A ratio compares one thing to another and can be written like 3 to 2, 3:2, and 3/2.

Examples:

• -1.55555...(with a repeating 5)

• 4/5

• 6 5/6

• -100 7/20

• 4.56789

Rational numbers in the real world:

• $8,236.55 in my bank account. Been saving! 🏦

• 32.777...º Celsius or 91º Fahrenheit today 😎🏖

• Only 1 and 3/4 miles from home to the park 🚲🌳

Irrational numbers are non-terminating decimals without a pattern. This means that they continue on and on without end. Also, the key is that they don't have a repeating pattern.

They're usually found in a form that includes a mathematical symbol, like π (pi), or √ (square root). These numbers aren't from a ratio or fraction.

Examples:

• π — starts with 3.1415926535 but keeps going and going

• √2 — starts with 1.4142135623 but keeps going and going

• √21 — starts with 4.5825756949 but keeps going and going

• e — Euler's number, starts with 2.7182818284 but keeps going and going

• ϕ — The Golden Ratio, starts with 1.618033988749 but keeps going and going

Irrational numbers in the real world:

These are hard to spot in the real world but are used in interest with money, construction with circular objects, and design/engineering with precise calculations.

Numbers can be one type or multiple types.

2 is a whole number, an integer, and a rational number while 9.7 is only a rational number.

Check out this table for more examples:

Square Root Special Note:

In the example √9, the square root of 9 is 3 (because 3 times 3 is 9) and 3 is a whole number, an integer, and a rational number. However, √7 is approximately 2.6457513110 but continues on (non-terminating) without a pattern so is irrational.

Now that you know about the types of numbers, there's no limit to what you can do in math!

Check out these Bytes and other resources to see what else you can do with numbers: