# Dividing Decimals

## Related calculator: Long Division Calculator

It is pretty easy to **divide decimals** after learning dividing decimals by whole numbers and dividing whole numbers by decimals.

To use techniques from these notes, simultaneously move decimal points to the right, until you get at least one whole number.

**Example 1**. Calculate $$${11.5}\div{4.6}$$$.

Simultaneously move decimal point one position to the right: $$${115}\div{46}$$$.

We obtained two whole numbers, so can perform long division as always: $$${115}\div{46}={2.5}$$$.

Thus, **$$${\color{purple}{{{11.5}\div{4.6}={2.5}}}}$$$.**

Now, let's see an example which leads to dividing decimal by a whole number.

**Example 2**. Calculate $$${7.68}\div{2.4}$$$.

Simultaneously move decimal point one position to the right: $$${76.8}\div{24}$$$.

We obtained one whole number and now can divide decimal by a whole number: $$${76.8}\div{24}={3.2}$$$.

So, **$$${\color{purple}{{{7.68}\div{2.4}={3.2}}}}$$$.**

Final example leads to dividing whole number by a decimal.

**Example 3**. Calculate $$${16.54}\div{3.308}$$$.

Simultaneously move decimal point two positions to the right: $$${1654}\div{330.8}$$$.

We obtained one whole number, so can divide whole number by a decimal: $$${1654}\div{330.8}={5}$$$.

Thus, **$$${\color{purple}{{{16.54}\div{3.308}={5}}}}$$$.**

Now, it is time to practice:

**Exercise 1**. Find $$${3.8}\div{1.9}$$$.

**Answer**: 2.

**Exercise 2**. Calculate $$${32.4}\div{0.16}$$$.

**Answer**: 202.5.

**Exercise 3**. Find $$$-{0.025}\div{2.5}$$$.

**Answer**: -0.01.

**Exercise 4**. Find $$$-{5.95}\div{\left(-{2.8}\right)}$$$.

**Answer**: 2.125.

**Exercise 5**. Find $$${3.4}\div{0.008}$$$.

**Answer**: 425.