PRINCÍPIO POSICIONAL - SISTEMAS DE NUMERAÇÃO 6°ANO - AULA 07

X-Math

há 4 semanas

Você já parou para pensar por que a posição de um número muda completamente o seu valor? 🤔
Neste vídeo, vamos entender o que é um sistema de numeração posicional, um dos conceitos mais importantes da matemática e base para todos os cálculos que fazemos no dia a dia.

O sistema posicional é aquele em que o valor de cada algarismo depende da posição que ocupa. O exemplo mais conhecido é o sistema decimal (ou indo-arábico), utilizado em todo o mundo. Nele, cada casa representa uma potência de 10 — unidades, dezenas, centenas e assim por diante.

Nesta aula, você vai descobrir:

O que é um sistema de numeração posicional;

Como funciona o sistema decimal;

Por que o valor de um número muda conforme sua posição;

A relação entre os algarismos e as potências de 10;

E como esse sistema revolucionou a forma como representamos os números.

📘 Ideal para estudantes do ensino fundamental e para quem quer entender de forma clara e prática os fundamentos da matemática.

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00:00The positional principle—now let's talk about this principle. I'll start here.

00:12Now I'm showing you two numbers, and let's understand how it works. You're seeing two there now.

00:22The numbers 235 and 253, but it's important to mention that although these two numbers are written with the same characters...

00:35In digits, the relative value of each digit varies according to its position in a written document.

00:43So let's understand how this works. We have here 235. 235 means two hundred.

00:53Three tens and five units, correct? Now let's write these numbers here in another way so...

01:02If you understand this principle, we have two abacuses here now, as you can see if you're not familiar with them.

01:09So, go to the card and watch our lesson about the abacus, or the link is also there.

01:15So, in the description, let's go. We have these two abacuses. Notice that on the first rod of this abacus we have...

01:23There are three rings on the second rod, five on the third, two rings on the third, and there are none here now.

01:33We have five rings on the first, three on the second, two on the third, and zero on the fourth, so reflecting on...

01:44This abacus, we can say that in this abacus here we have three units, five tens, and two hundreds, therefore we have...

01:54235, so you realize that here it's 253 and here it's 235, so you can already see that the principle...

02:18limited by the modal system, it is determining the position of each digit, so if the 5 is in the place of

02:26So the tens digit is 50, and if the 3 is in the tens place, then it's 30. That's why here we have two hundred and

02:35thirty-five, we already have two hundred and fifty-three here, let's move on now, let's talk about zero, you already

02:48I heard that phrase, "You're a nobody," when someone is there in a discussion.

02:53heatedly, she utters these words intending to offend even the other person, saying, "You're a nobody."

03:02So let's understand why there's a leading zero, right? So let's see what mathematics says.

03:07It teaches us about this. Let's go. We have this Saturday here, and I'll put another one next to it as well.

03:17In other words, we have these two abacuses here. The one here, in the first position, has three rings, this one doesn't.

03:25None, there are two here and the other one has none. The one over here has already changed position. The first position is not

03:33The first one has no rings, the second has three rings, the third has two, and the first has none.

03:40Ring, right? So we can already highlight this piece of evidence that we observed here. Zero,

03:47Two, zero, and three. Here, we have zero, two, three, and zero. That is, in the first position it's zero, in the second...

03:59Three tens, in the other two hundreds. Here now it's three units, zero tens, two hundreds and zero.

04:09thousand. So, here you can already get an idea that when we talk about the zero on the left, it means the zero

04:17When it's to the left of a number, it practically has no effect; it doesn't change the value.

04:24of the number, because here we have 203 and here we have 230. Notice that the zero to the left of both of them...

04:31Numbers won't affect the value. Now, the zero to the right, you can see that it does affect it. If you

04:38Adding more zeros between the numbers on the right will definitely affect it. And now let's go.

04:44To represent it another way. We are representing it here with two plates of one hundred and three unit cubes.

04:52So we have 203. This material here, for those who don't know, also includes a lesson. You can find it here in the card.

04:59which is about golden material. And here now we have the representation of 230, which are two plates of one hundred small cubes,

05:08and three bars of thirty. Each bar has ten small cubes. So, we can now write it in an expressive form.

05:17203 is equal to 2 times 100, which is 200, plus 0 times 10, which is this, which is 0, plus 3 times 1.

05:30Therefore, this equals 203. The other number, we have that 230 is equal to 2 times 100. 200 is here. 3 times 10 is here, 30.

05:43And what do we have here? We have 0 times 1, which equals 0. So, we have 230. And now, I'm going to propose a challenge to you.

05:54You all understood the idea here of the positional principle. That is, the position where the digit is located,

06:02It can affect the value of the number. And you noticed that the leading zero doesn't represent anything.

06:10So now, let's move on to the challenge.

06:15Given the numbers 235, 523, and 352, what is the value of the digit 3 in each number?

06:29That is, in 235, the number 3 is here in the second position.

06:36What would this amount be? That's what I want to know.

06:40So, go ahead and leave your answer in the comments.

06:44Here, for example, is 523. It's in first place.

06:49In the first position, it is unity.

06:52So, what is the value of a digit 3 that is in the first units position?

06:59There are three units. Therefore, what number is it?

07:02Go to the comments and post it.

07:03And here, now, we have 352.

07:08The digit 3 is in the third position, in the hundreds place.

07:13So, what value corresponds to the digit 3 in the hundreds place?

07:20So, go to the comments and put the answer, I want to know.

07:24Finally, I ask that you subscribe to the channel, activate the notification bell, and share our videos.

07:32This video, in particular, is for those who don't understand why there's a leading zero.

07:37When someone calls, are you a nobody?

07:40So now you understand why there's a zero on the left.

07:44It does not change the value of the number.

07:46So, the lesson ends here.

07:51See you next time.

07:51And there

07:56And there

07:57And there

07:58Thanks.

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