Question

If we divide 100 by 3 then we get 3.333.......
But if we multiply 3.33333......Back by 3 we get
9.99999...... Why and how?

Answer 1

Hey mate here is your answer .

It is because when we divide 10 by 3 , we get 3.3333..... but this answer is not accurate .That is the reason why we get 9.999.... after multiplying .

❤Hope it helps you ❤

Answer 2

Yes. Its true that when we divide 100 by 3, we obtain 3.33333... It can also be written as

$3.\bar{3}$

Also, when we multiply 3.3333.... by 3, we get 99.9999..... and not 100. Yes. That is also true.

Numbers like 99.999.... and 3.333..... are rational numbers and they are said to be repeating recurring decimals. They can be converted in the form of p/q, where q is not 0.

Lets convert 99.999.... in the form of p/q, where q is not 0.

Let 99.9999 be equal to x.

Then,

x = 99.9999.... -(eqn.1)

Multiplying both sides by 10, we have,

10x = 999.9999.... -(eqn.2)

Subtracting eqn.1 from eqn.2, we have

10x - x = 999.9999.... - 99.9999..... = 900

Or, 9x = 900

Or, x = 900/9 = 100

But, x = 99.999.....

Thus, 99.999999..... = 100

This means, when we divide 100 by 3, we get 3.3333 and when we multiply it by 3, we get 99.9999, which in turn is equal to 100.

This satisfies yor question.