Question

What is the decimal equivalent of $\dfrac{5}{12}$ ?

Answer 1

Hint: To solve these types of questions where it is required to write a fraction form in a decimal form, we just simply need to divide the numerator by the denominator and simplify the expression to its lowest form. Then we will get our required solution.

Complete step by step solution:
The given fraction is: $\dfrac{5}{12}$
In fractions, the number that is written above the line is called the numerator and the number written below the line is known as the denominator.
The division in a fraction is represented by the line between the numerator and denominator.
 As we can see that $\dfrac{5}{12}$ is already in its lowest form, which means we cannot simplify it further by cancelling out the terms.
Also, the factors of the denominator are $2\times 2\times 3$ , which are not factors of $5$, therefore we will have to long divide $5$ by $12\;$ and the final answer will have some repeating numbers as well after the decimal point.
To perform the long division on the given fraction, write the numerator as the dividend and the denominator as the divisor.
The next step we should include finding a multiple of divisor which should be smaller than or equal to the given dividend.
Write the multiple of the divisor as the quotient and find the remainder by subtracting both the numbers.
If the new dividend is smaller than the divisor then you should put a decimal in the quotient and add a zero in the dividend.
Now, repeat the same steps till you get the remainder as zero, and if the remainder keeps on repeating then just put a bar on the quotient.
$\Rightarrow \dfrac{5}{12}=0.4166...$
After we use the long division method, we can see that the last digit, that is, $6$ keeps on repeating, hence it can also be written as $0.41\overline{6}$ .
Therefore, the decimal equivalent of $\dfrac{5}{12}$ is $0.4166..\;$ or $0.41\overline{6}$ .

Note: When we convert fractions into decimals, there are generally three types of decimal fractions, which include terminating decimals, recurring (or repeating) decimal fractions, and non-terminating decimal fractions.
In the above solution, we have a recurring or repeating decimal fraction, since one digit keeps on repeating in the quotient. In terminating decimal fractions, we have a finite number of digits in the quotient and in non-terminating decimal fractions the digits go on and the division does not end.