Dividing 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.