Question

How do you turn $\dfrac{2}{3}$ to a decimal?

Answer 1

Hint: One way of writing a fraction as a decimal is to change the fraction so the denominator is a power of 10. This is possible only If the denominator has $2$ and $5$ as prime factors.
However, 3 is a prime number itself and also does not divide 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 answer:
According to the given information, we need to turn $\dfrac{2}{3}$ to a decimal.
One possible way to rewrite $\dfrac{2}{3}$ is $2 \div 3$ .
On dividing both the numbers, we get
$3\underline {\left| 2 \right..00000000000} 0$
$0.666666666666.....$
Each time the remainder is $2$, the pattern continues to infinity.
This is rounded off to an appropriate level of accuracy to provide an answer.
$\dfrac{2}{3} = 0.67$or $\dfrac{2}{3} = 0.667$ etc.
 Therefore, $\dfrac{2}{3}$can be written as $0.67$ in decimal form.

Additional Information: It is always better to look at the denominator first when we need to convert a fraction into decimal. If the denominator only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in a power of 10 and the result will be a limiting decimal. 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.

Note: It is always better to look at the denominator first when we need to convert a fraction into decimal. 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.