What Is the Number System? Place Value Explained Simply

The number system is the set of rules we use to write and read numbers. Ours uses exactly ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. That's it. Those ten digits are the entire alphabet of maths.

Here's the strange part. These symbols aren't natural laws. They're agreed-upon shapes that humans settled on over centuries. The cleverness isn't in the digits themselves. It's in how we arrange them.

Because we use ten digits, our system is called base 10, or the decimal system. The word decimal comes from the Latin word for ten.

• Ten digits: 0 to 9
• Base 10, also called the decimal system
• Any number, however big, is built from these ten symbols

Place value means a digit's value depends on where it sits. The digit 5 alone means five. Put it in 50 and it means fifty. Put it in 500 and it means five hundred. Same symbol, very different power.

Let's take 352. Reading from the right, the 2 sits in the ones column, so it's worth 2. The 5 sits in the tens column, so it's worth 50. The 3 sits in the hundreds column, so it's worth 300. Add them up: 300 + 50 + 2 = 352.

See? Simple! The number isn't three-five-two. It's three hundred, plus fifty, plus two.

Count with me: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Now what? We've used every digit we have. So we reset the ones column back to 0 and add a brand-new column to the left: 10.

That's called carrying over. The ones column restarts, and the tens column gains a 1. The same thing happens at 99. We reset both columns to 0 and add a hundreds column: 100.

This is why the system never runs out. Whenever we hit a wall, we simply open a new column on the left. Ten digits, but endless room to grow.

Each column to the left is exactly ten times the value of the one before it. Ones is ×1, tens is ×10, hundreds is ×100, thousands is ×1000, and on it goes.

Why ten? Because we have ten digits. After ten ones, we carry one into the tens. After ten tens, we carry one into the hundreds. The base and the columns are two sides of the same coin.

This pattern repeats forever. There's no largest column. Lakhs, crores, and beyond all follow the same rule.

• Ones column: digit × 1
• Tens column: digit × 10
• Hundreds column: digit × 100
• Thousands column: digit × 1000
• Each step left multiplies the value by 10

Here's the payoff. With ten digits and the position trick, you can write any number, no matter how huge. A googol, which is a 1 followed by 100 zeros, needs only two different digits: 1 and 0.

The number of possible numbers isn't limited by how many digits we have. It's limited by how many columns we're willing to write. And there's always room for one more column on the left.

So the number system isn't about memorising big numbers. It's a position game. Ten symbols, endless combinations.

Our system is so effective that the whole world adopted it. But it's just one option among many. A system can be built on any base.

Computers use base 2, called binary, with only two digits: 0 and 1. It's the same position trick, just with a smaller alphabet. In binary, each column to the left is two times bigger, not ten times.

Why do computers use two? Because a switch in a circuit has two easy states: on and off. Two states map perfectly onto two digits. So binary isn't simpler maths. It's maths that fits the hardware.