Question

How do you convert $\dfrac{4}{{15}}$ to a decimal?

Answer 1

Hint: It is always better to look at the denominator first when we need to convert a fraction into decimal. If a denominator only has $2$ and $5$ as prime factors, one way of writing a fraction as a decimal is to change the fraction so the denominator is a power of $10$ . In case it has a prime factor other than $2$ and $5$ , conversion to decimal could be longer and will result in an infinite loop with repeating decimals.
However, $15$ does not divide or multiply into any power of $10$ , so that method does not work here.
In case it has a prime factor other than $2$ and $5$ , conversion to decimal could be longer and will
result in an infinite loop with repeating decimals.

Complete step by step solution:
According to the given information, we need to turn $\dfrac{4}{{15}}$ to a decimal.
One possible way to rewrite $\dfrac{4}{{15}}$ is 4÷15
On dividing both the numbers, we get
$15|4.000000$
$0.26666.....$
After the first one steps in the division each the pattern continues to infinity.
This is rounded off to an appropriate level of accuracy to provide an answer.
$0.2667$
Therefore,
$\dfrac{4}{{15}}$ can be written as $0.2667$ in decimal form.

Note: As you can see if the denominator only has $2$ and $5$ as prime factors, it becomes very easy to solve this question. So, before solving any question you must first think and remember all the basic things.