Question

How do you turn $\dfrac{8}{9}$ 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, $9$, when is factorized, gives two $3$’s as it’s factor, which is a prime number itself. Also, $'9'$ 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 $\dfrac{8}{9}$ to a decimal.
One possible way to rewrite $\dfrac{8}{9}$ is $8 \div 9$ .
On dividing both the numbers, we get
\[9\underline {\left| 8 \right..000000000} 0\]
   $0.8888888888.....$
Each time the remainder is $8$, the pattern continues to infinity.
This is rounded off to an appropriate level of accuracy to provide an answer.
$\dfrac{8}{9} = 0.889$or $\dfrac{8}{9} = 0.89$ etc.
Therefore, $\dfrac{8}{9}$can be written as $0.889$ 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: To convert a fraction into decimal, it is always better to look at the denominator first. 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.