What's the difference between real numbers and integers?

Look at these numbers:

You might be wondering...are these even real??? 🤔

They don’t all look the same.

Some feel “normal" — like 3.

Others look a bit strange — with decimals, fractions, or symbols like √.

Have you ever heard the terms real numbers and integers?

You might be surprised to learn how they're connected — and what sets them apart.

Let's explore how these groups of numbers compare.

Imagine you're climbing a staircase.

You can go up the steps (positive numbers) or down below the ground (negative numbers).

And there's one step at ground level — zero.

But notice — you can’t stand on half a step or 2.5 steps — that would be pretty awkward, right? 😀

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Integers include:

• positive whole numbers like 1, 2, 3,...

• negative whole numbers like -1, -2, -3,...

• zero

Real-life examples of integers:

• 4 coins in your wallet

• 30 students in a class

• 0 new messages

• -2 floors below ground

These are integers because they are complete numbers with no decimals or fractions.

Real-life examples of non-integers:

• 2.5 hours of screen time

• 1/2 meters of rope

• -30.33°C on a thermometer

• 1.75 gallons of juice

These aren't integers because they're not whole quantities.So, what kind of numbers are they? Let's find out!

Real numbers are all the numbers you can find on a number line.

They include:

• Integers like -3, 0, 5

• Decimals like 1.4, 2.46, -10.8

• Fractions like 1/2, 7/10, 5/6

• Numbers that go on forever, such as:

  • Repeating decimals like 0.333333.... (also written as 0.3̅ )

  • Non-repeating decimals like √2 or π

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All these numbers belong to one big family called "real numbers".

Real numbers are everywhere — in your bank account, temperatures, recipes, distances, and many more. 📌

All integers are real numbers, but not all real numbers are integers.

Let's take another look at the number line:

The big solid marks (-4, -3, -2, -1, 0, 1, 2, 3, 4,...) are the integers, whereas real numbers include all the integers and everything in between.

For example, numbers like -2.5, 0.75, 1.33, and 3.14 are all real numbers — they have decimals or fractions that fit between the whole-number spots.

Try these steps to explore the difference between real numbers and integers: