So what is important to understand here?

Let's start with some example, simple example.

Imagine you want to find the two-digit number that becomes

seven times smaller when the first digit is deleted.

Well, it's a very easy question because there is not so

many two-digit numbers, and also it should be divisible by seven.

So if you remember the multiplication table, the first two-digit number is 14,

and then they go, and then you get 63, and the next one is 70,

and then division by seven gives 10, which is not one digit.

So it's simple small list, and

you can check that 35 is the only thing, and if you're asked for

something more complicated, for example imagine we asked you for

a number that becomes 57 times smaller when the first digit is deleted.

It's then, it's not so easy, and what is important that if you come

next day and say, look here is the number, then you are done.

We have no right to ask you why you choose this number, and how you found it.

So it's just you give an example, we check the example,

and we should be completely satisfied, and this is from the student's view.

But of course the teachers is usually,

the teachers do not have the rights the student have.

So if you are teacher, then you should explain how you find that solution,

and now we'll try to explain how you can do this.

So, let's write again what do we want.

We, here is the number.

Here is the first digit, which should be deleted.

This is what remains, and

this is our equation shows what should be achieved.

Okay, but this is not very common for algebra because there is some dots here so

the number is written in a decimal notation,

it's not very good, so let's write something.

Note this part by X, and then on the right-hand side,

we have 57 X, it's easy, but on the left-hand side,

we have X + a0...0, and we need k zeros,

and what is important, that if we add one 0,

this means that we multiply a by 10.

So actually, this thing is just a x 10 to the number of zeros,

and we will write it now.