**On this Page**:1. Dividing by a Power of 10

2. Dividing by other Numbers

3. Dividing by a Decimal Number

Dividing decimal numbers in Math is similar to dividing whole numbers, one just has to pay attention to the position of the decimal point when dealing with dividing decimals examples.

### Dividing by a Power of 10:

When dividing a decimal number by 10 or a power of 10 such as 100 or 1000, the process follows a pattern which keeps things fairly simple.

How large the power of 10 dividing is, decides how many places to the left that the decimal point moves, resulting in the solution.

Dividing by

**10**: Decimal point moves 1 place to the left.

Dividing by

**100**: Decimal point moves 2 places to the left.

Dividing by

**1000**: Decimal point moves 3 places to the left.

And so on.

__Examples__

*(1.1)***3.4**÷

**10**=

**0.34**

*(1.2)***2.5**÷

**1000**=

**0.025**

*(1.3)***0.6**÷

**100**=

**0.006**

*(1.4)***0.082**÷

**10’000**=

**0.0000082**

*(1.5)***0.409**÷

**1000**=

**0.000409**

## Dividing Decimals Examples,

Dividing by other Numbers

When you want to do a division sum such as 7.66 ÷ 3.

This can be dealt with like it was 766 ÷ 3,

care just has to be taken with where the decimal point goes in proceedings.

__Examples__

*(2.1)***7.86**

**÷ 6**

*Solution*First step is to set up as a normal division sum.

**6**

**7.86**

Next we place a decimal point in the position where the answer will be, directly above the place of the decimal point in the dividend part.

**.**

**6**

**7.86**

Now from here it’s just standard division as normal.

**1. 31**

**6**

**7.**,

^{1}86**7.86**÷

**6**=

**1.31**

*(2.2)***13.86**

**÷ 3**

*Solution***3**

**13.86**

.

**3**

**13.86**

**04. 62**

**3**

**13.**,

^{1}86**18.33**÷

**3**=

**6.11**

## Dividing by a Decimal Number

When encountering dividing decimals examples that require division by a decimal number, it’s handy to change the decimal number that you’re dividing by to a whole number.

This can be done with multiplication, though both numbers in the sum must be multiplied by the same number.

An example of a sum with decimal division is

6 ÷ 0.4.

Multiplying both numbers in the sum by 10 won’t change the overall sum itself,

but it does change the sum appearance.

Changing it to 60 ÷ 4, which can be worked out as 15.

__Example__

*(3.1)***392**÷

**1.4**

*Solution*We can look to change 1.4 to a whole number, which can be done by multiplying both numbers in the sum by 10.

**1.4**×

**10**=

**140**

**392**×

**10**=

**3920**

We now have 3920 ÷ 14.

Which we can solve by standard Short Division.

**02 80**

**14**

**39**

^{11}20We have an answer of 280.

**392**÷

**1.4**=

**280**

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