Question

How do you write each fraction or mixed number as a decimal: \[{3}/{11}\;\]?

Answer 1

Hint: Let a fraction be \[\dfrac{p}{q}\] where p and q are coprime. If the p, q is not coprime then we have to make them coprime by the elimination of the factors common in both the numerator and denominator. Most of the fractions can be converted into a decimal by making the denominator of the fraction form multiples of 10.

Complete step by step answer:
According to the given question, we are given a number in the form of \[\dfrac{p}{q}\]. Let it be taken as ‘a’ = \[\dfrac{3}{11}\].
Here, we can see that 3 and 11 are not coprime. The denominator is 11 we cannot convert 11 into multiples of 10. So, we divide the numerator with the denominator. We divide it using a long division method.
Then the value of \[\dfrac{3}{11}\] in decimal is \[0.27272727..........\].
If any value after the decimal is repeating. For example \[0.ababab.....\] then we can write the decimal as \[0.\overline{ab}\].
So, now we can write the given decimal of the fraction \[\dfrac{3}{11}\] in the form above.
Here the value 27 after the decimal is repeating. So we can write it as
\[\Rightarrow \]\[\dfrac{3}{11}=0.\overline{27}\]
Therefore, the fraction \[\dfrac{3}{11}\] in decimal form is \[0.\overline{27}\].

Note:
 We can do the conversion of a fractional number into a decimal by simply dividing the numerator of the fraction form with the denominator. We can also do the conversion of a fraction into a percent by multiplying it by 100 and then simple division. While calculating decimal form we must round the decimal part.