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

🏆Practice multiplying and dividing decimal fractions by 10, 100, etc.

In multiplications: the decimal point moves to the right as many steps as the number has zeros.
In divisions: the decimal point moves to the left as many steps as the number has zeros.

Start practice

Test yourself on multiplying and dividing decimal fractions by 10, 100, etc.!

einstein

\( \text{0}.07\times10= \)

Practice more now

Multiplication and division of decimal numbers by ten, hundred, etc.

Multiplying and dividing decimal numbers by 1010, 100100, 10001000 and even 1000010000 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 1010, 100100, 1,0001,000 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:

0.7×10=0.7\times 10=
We will ask ourselves:
How many zeros does the multiplied number have? (How many zeros are in the number 1010?) – The answer is 11.
Therefore, we will move the decimal point one step to the right in this way:

1a- we will move the decimal point one step to the right in this way

0.7×10= 0.7\times 10=

Observe: we have moved the decimal point one step to the right and obtained 0707
The 00 before the 77 means nothing, therefore, we can remove it.
Also, after the decimal point there is nothing, that is, 00 therefore we simply have a 77!
So, the solution is: 0.7×10=70.7\times 10=7


Example 1

0.486×100=0.486\times 100=
We will ask ourselves:
How many zeros does the multiplied number have? (How many zeros are in the number 100100?) – The answer is 0.486×100= 0.486\times100= .
Therefore, the decimal point will move 22 steps to the right.
We will obtain:

2a- the decimal point will move 2 steps to the right

0.486×100= 0.486\times 100=

We will realize that the 00 to the right of the point is canceled out, therefore, the answer is: 48.648.6


Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Example 2

4.857×1000= 4.857\times 1000= 

We will ask ourselves:
How many zeros does the multiplied number have? The answer is 33.
Therefore, the decimal point must be moved 33 steps to the right.
We will move it and obtain:

3a - How many zeros does the multiplied number have

4.857×1000= 4.857\times 1000=

Observe, we have moved the decimal point 33 steps to the right and obtained 4857.4857.
There is nothing to the right of the decimal point, that is, there is zero, so the answer will simply be 48574857


Example 3

1.495×10000=1.495\times 10000=
We will ask ourselves:
How many zeros does the multiplied number have? The answer is 44.
Therefore, we will move the decimal point 44 steps to the right and we will obtain:

4a - we will move the decimal point 4 steps to the right and we will obtain

1.495×10000= 1.495\times 10000=

Observe, we have moved the decimal point 44 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​0 in the empty space and we will arrive at the answer being 1495014950.


Do you know what the answer is?

Important aspects

In multiplication

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​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 1010, 100100, 1,0001,000 etc:

The method to solve divisions of decimal numbers by 1010, 100100, 1,0001,000 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.

Now let's solve an exercise

0.610=0.6∶10=

We will ask ourselves:
How many zeros does the number by which we are dividing have? (That is 1010
The answer is 11.

Therefore, we will move the decimal point 11 step to the left
and we will obtain:
0.610=0.6∶10=

5a - we will move the decimal point 2 steps to the left and we will obtain

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 00 (marked in green).


Check your understanding

Exercise 1

0.364:100=0.364:100=
We will ask ourselves:
How many zeros does the number by which we are dividing have? The answer is 22.
Therefore, we will move the decimal point 22 steps to the left and we will obtain:

6a - we will move the decimal point 2 steps to the left and we will obtain

0.364:100= 0.364:100=

Observe, we have moved the decimal point 22 steps to the left and filled the empty places with 00.


Exercise 2

67.683:1000=67.683:1000=
How many zeros does the number by which we are dividing have? 33.
Therefore, we will move the decimal point 33 steps to the left and we will obtain:

7a - we will move the decimal point 3 steps to the left and we will obtain

67.683:1000= 67.683:1000=


Do you think you will be able to solve it?

Exercise 3

54.12:10000=54.12:10000=
There are 44 zeros, therefore, the decimal point will move 44 steps to the left.
We will obtain:

8a - the decimal point will move 4 steps to the left

54.12:10000= 54.12:10000=


Test your knowledge

examples with solutions for multiplying and dividing decimal fractions by 10, 100, etc.

Exercise #1

0.07×10= \text{0}.07\times10=

Video Solution

Answer

0.7 0.7

Exercise #2

1.004×10= 1.004\times10=

Video Solution

Answer

10.04 10.04

Exercise #3

111.1:10= 111.1:10=

Video Solution

Answer

11.11 11.11

Exercise #4

1.14×10= 1.14\times10=

Video Solution

Answer

11.4 11.4

Exercise #5

11.31:10= 11.31:10=

Video Solution

Answer

1.131 1.131

Start practice