Dividing and expressing the answer as a decimal

In a nutshell

A decimal is a way of writing a non-whole number. Non-whole numbers appear "in between" whole numbers. For example, $3.5$ is in between the whole numbers $3$ and $4$ . They are shown by the presence of a decimal point and at least one digit greater than $0$ following this decimal point. You can divide whole numbers completely (without using remainders) to get a decimal.

Converting a fraction to a decimal

Decimals can be written as fractions. Any given fraction can be also written as a decimal. There are many ways that you can convert a fraction into a decimal.

Dividing using equivalent fractions

Equivalent fractions are fractions that represent the same value, so they are are worth an equal amount. If you multiply or divide the numerator (top number) and the denominator (bottom number) by the same value, your answer will be an equivalent fraction. When working with decimals, it can sometimes be easier to change the denominator to a value of $10$ or $100$ . This way, you can easily find out the fraction in decimal form.

PROCEDURE

1.	Find out the number you need to multiply (or divide) the denominator by to get either $10$ or $100$ .
2.	Multiply (or divide) the numerator with the answer from Step 1.
3.	Calculate the decimal by dividing the new numerator by the new denominator.

Example 1

What is $\dfrac{12}{50}$ in decimal form?

Calculate the value needed to multiply the denominator with to reach $100.$

$50 \times 2 = 100$

Multiply both the numerator and denominator by $2$ .

$\dfrac{12}{50} \times \dfrac{2}{2}= \dfrac{24}{100}$

Divide the numerator by the denominator.

$24 \div 100 = \underline{0.24}$ 

Example 2

Convert $\dfrac{7}{20}$ into a decimal.

Calculate the value needed to multiply the denominator to reach $100.$ 

$20 \times 5 = 100$ 

Multiply both the numerator and the denominator by $5$ .

$\dfrac{7}{20} \times \dfrac{5}{5} = \dfrac{35}{100}$

Divide the numerator by the denominator.

$35 \div 100 = \underline {0.35}$ 

Short division

Short division can be used to divide larger numbers. It is often referred to as the "bus stop method", as it appears as the number which is being divided is inside a bus stop. To divide to get a decimal, you should not use remainders, but add a decimal followed by place holder zeros under the bus stop. You can then "carry" the remainder over to the right and do this until there are no more remainders.

PROCEDURE

1.	Place the number being divided (first number) under the bus stop. Place the number you are dividing by outside to the left of the bus stop.
2.	Complete the initial division as normal, but do not give the answer with a remainder.
3.	Add a decimal point both underneath and on top of the bus stop, in line with one another.
4.	Add as many place holder zeros as needed underneath the bus stop.
5.	Carry any remainder over to the place holder zero to the right, until you no longer have a remainder.

Note: You can add as many zeros to the number under the "bus stop" as you like, without changing the number's value.

Example 3

What is $67 \div 4$ ? Give your answer as a decimal.

Place the number being divided, the first number, under the bus stop. Place the number you are dividing by, the second number, outside the bus stop.

$4\overset{}{\overline{\smash{)}67}} \\$

Complete the initial division as you would normally, carrying over any remainders onto the next number.

$4\overset{\ \ 1\ \ 6 \ r \ \ 3 }{\overline{\smash{)}6^27 \ \ \ \ }} \\$

The question asks for the answer as a decimal. Therefore, add a place holder zero and carry the remainder over.

$4\overset{ \ \ 1\ 6 \ . \ \ 7r \ 2 }{\overline{\smash{)}67.^30 \ \ \ \ }} \\$

There is still a remainder, so add another place holder zero and carry this over.

$4\overset{ \ \ 1\ 6 \ . \ \ 7 \ \ \ 5 }{\overline{\smash{)}67.^30 ^20 }} \\$ 

There is no remainder for this step, so this gives you the final answer.

$67 \div 4 = \underline{16.75}$ 