Multiplication and Division of Decimal Numbers by 10, 100, etc.

Multiplying and dividing decimal numbers by $10$, $100$, $1000$ and even $10000$ is such a simple matter that, if you practice a little, you will know how to solve these types of exercises even in your sleep! Shall we start?

Multiplication of decimal numbers by $10$, $100$, $1,000$ etc:

The key to this type of multiplication exercises is to remember that the decimal point slides to the right as many steps as there are zeros in the number by which the decimal number is multiplied.
See how simple this is:

$0.7\times 10=$
We will ask ourselves:
How many zeros does the multiplied number have? (How many zeros are in the number $10$?) – The answer is $1$.
Therefore, we will move the decimal point one step to the right in this way:

$0.7\times 10=$

Observe: we have moved the decimal point one step to the right and obtained $07$
The $0$ before the $7$ means nothing, therefore, we can remove it.
Also, after the decimal point there is nothing, that is, $0$ therefore we simply have a $7$!
So, the solution is: $0.7\times 10=7$

$0.486\times 100=$
We will ask ourselves:
How many zeros does the multiplied number have? (How many zeros are in the number $100$?) – The answer is $0.486\times100=$.
Therefore, the decimal point will move $2$ steps to the right.
We will obtain:

$0.486\times 100=$

We will realize that the $0$ to the right of the point is canceled out, therefore, the answer is: $48.6$

$4.857\times 1000=$

We will ask ourselves:
How many zeros does the multiplied number have? The answer is $3$.
Therefore, the decimal point must be moved $3$ steps to the right.
We will move it and obtain:

$4.857\times 1000=$

Observe, we have moved the decimal point $3$ steps to the right and obtained $4857.$
There is nothing to the right of the decimal point, that is, there is zero, so the answer will simply be $4857$

$1.495\times 10000=$
We will ask ourselves:
How many zeros does the multiplied number have? The answer is $4$.
Therefore, we will move the decimal point $4$ steps to the right and we will obtain:

$1.495\times 10000=$

Observe, we have moved the decimal point $4$ steps to the right, but we have been left with an empty space to the left of the point.
Then, we will add a $​0$ in the empty space and we will arrive at the answer being $14950$.

We will move the decimal point to the right.
We will ask how many zeros the multiplied number has, that will give us a clue on how many steps to the right the point should move.
If when counting the steps we see that there is nothing to the right of the decimal point (that is $​0$) we will simply discard the decimal point and the answer will be just the number we obtained.
If we got an answer that leaves an empty space to the left of the decimal point we will add a zero and take it into account for our result.

Division of decimal numbers by $10$, $100$, $1,000$ etc:

The method to solve divisions of decimal numbers by $10$, $100$, $1,000$ etc. is very similar to the way we have learned to solve multiplication exercises.
The only difference is where the decimal point slides.
In these types of division exercises, the decimal point slides to the left as many steps as there are zeros in the number by which the decimal number is divided.

$0.6∶10=$

We will ask ourselves:
How many zeros does the number by which we are dividing have? (That is $10$) 
The answer is $1$.

Therefore, we will move the decimal point $1$ step to the left
and we will obtain:
$0.6∶10=$

Observe, we have moved the decimal point one step to the left, but there is an empty space to the left of the decimal point, therefore we will fill it with a $0$ (marked in green).

$0.364:100=$
We will ask ourselves:
How many zeros does the number by which we are dividing have? The answer is $2$.
Therefore, we will move the decimal point $2$ steps to the left and we will obtain:

$0.364:100=$

Observe, we have moved the decimal point $2$ steps to the left and filled the empty places with $0$.

$67.683:1000=$
How many zeros does the number by which we are dividing have? $3$.
Therefore, we will move the decimal point $3$ steps to the left and we will obtain:

$67.683:1000=$

$54.12:10000=$
There are $4$ zeros, therefore, the decimal point will move $4$ steps to the left.
We will obtain:

$54.12:10000=$