Zero · Lập trình với Martin

The number for nothing. Zero can do magic: adding it changes nothing, and it holds a place in writing.

The number for nothing at all

How many elephants do you have in your room? None. And yet there is a number for that: zero. It is written 0.

Zero means nothing. An empty bowl, an empty pocket, no goal.

It sounds simple, but zero is one of the cleverest numbers of all. On the number line it lives right at the start, before one.

And it can do magic. When you add zero, nothing happens: 7 + 0 = 7. When you subtract it, nothing again: 7 − 0 = 7. And when you subtract a number from itself, zero appears: 7 − 7 = 0.

People counted for a long time without zero and they kept getting mixed up. Then someone thought of giving nothing its own sign. Round nothing: 0. From then on you can write an empty bowl as easily as a full one. Clever, right?

But the most important job zero does is in writing numbers. Without it we would not tell 4 from 40.

Adam and Sofie play football in the garden. After the first half it is 3:0. “Zero means I did not score a single goal,” Adam frowns. Sofie comforts him: “Zero is a result too. Without it we could not write the score.” Then they count Adam’s pocket money: he had 20 Kč, he spent 20 on a ball keyring. “How much do you have left?” Adam peeks into an empty purse: “Zero Kč. Nothing at all.” “See,” Sofie laughs, “and it is still a number.” In the second half Adam scores two goals. “You can always bounce back from zero,” he says on the way home. The score and the purse both start at zero — and they grow.

💡

Add or subtract zero = leave the number alone. Zero adds nothing and takes nothing.

What zero can do

Zero has three important jobs.

1. Zero is a count. It answers the question “how many” when there is nothing. How many biscuits are left? Zero. It is a real number, not a hole.

2. Zero in calculating. The rules are three and all of them easy:

Number + 0 = the same number. 8 + 0 = 8. You added nothing.
Number − 0 = the same number. 8 − 0 = 8. You took nothing away.
Number − the same number = 0. 8 − 8 = 0. You took everything away.

3. Zero holds a place. In the number 40, zero says: four tens, no ones. If you left it out, a four would be left. In the number 105 (you will meet that later) zero holds the tens place. Without zero, writing numbers would fall apart.

On the number line, zero is all the way on the left, before one. Subtracting ends there: a result smaller than zero does not exist in our counting yet. That is why you cannot calculate 3 − 5 — from three sweets you cannot take five.

Flash questions with zero

9 + 0 = ? I add nothing. 9 stays.

0 + 6 = ? Nothing and six. It is 6.

7 − 0 = ? I take nothing away. 7 stays.

5 − 5 = ? I take everything away. 0 is left.

0 + 0 = ? Nothing and nothing. 0.

Every question with zero you solve at once. Just remember what zero does: nothing.

What zero is for in the number 30

I write 30. The three is 3 tens. Zero says: no ones.

Now I rub zero out. Left: 3. Three.

Thirty and three — a huge difference! Thirty sweets is a feast, three sweets is a moment.

Zero in 30 counts nothing, but it holds the three in the tens place. That is why it is called a place holder. Small job, big importance.

⚠️

Zero is not the same as the letter O. And watch: we cannot calculate 3 − 5 — from three things you cannot take five. If you need to go under zero, there is a mistake in the question or the numbers got swapped.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Bắt đầu with ten. If it goes well, add more.

Practise plus and minus to 10. Do not dodge zero!

Practise the questions

On paper

Paper and a pencil. It will be quick — zero is a fast number.

Calculate the flash questions: 4 + 0, 0 + 9, 6 − 0, 8 − 8, 0 + 0.
Write pairs of numbers and say the difference: 5 and 50, 7 and 70. What does zero do in them?
Find three situations at home where the answer is zero. For example: how many tigers do we have at home?
Draw a number line from 0 to 10. Mark where zero lives.

Now you 💪

I know that adding and subtracting zero does not change the number.
I know that a number minus the same number is zero.
I understand why zero in 40 holds the place.

✅

Done when: You solve ten flash questions with zero without a single pause.

What to take from this lesson

Zero = nothing. And it is a real number.
Plus zero and minus zero: the number does not change.
A number minus itself = zero.
Zero holds a place: 40 without zero would be 4.
We do not go under zero in our counting. 3 − 5 does not work.