Question

How do you simplify and make the fraction \[\dfrac{4}{33}\] into decimal?

Answer 1

Hint: We can also do this using basic simplification techniques. For simplifying it first we find GCF of both numbers. If GCF is more than \[1\] we have to divide both numerator and denominator with that number. If it is \[1\] then we have to divide the numerator with the denominator to make it into decimal form.

Complete step-by-step answer:
The given fraction is \[\dfrac{4}{33}\]
So to simplify it we have to find the GCF of both numbers \[4\]and \[33\]. To find the GCF we have to do prime factorization of the numbers.
\[4=2\times 2\]
\[33=3\times 11\]
We can clearly see that there are no common factors in their prime factorization. So it’s GCF is \[1\]
As already discussed if the GCF is \[1\] we have to divide our numerator with the denominator.
So in our case we have to divide \[4\] with \[33\].
Now dividing \[4\] with \[33\] will give the decimal form.
\[\dfrac{4}{33}=0.121212\]
As after the point \[12\] is repeating we can say \[0.121212\] as repeating decimal.
We can also represent it as \[0.\bar{1}\bar{2}\]
From this we can write
\[\dfrac{4}{33}\cong 0.\bar{1}\bar{2}\]
So the decimal form of \[\dfrac{4}{33}\] is \[0.\bar{1}\bar{2}\].

Note: We can also do this in a simple way without calculating the GCF. we can directly divide the numerator with the denominator. If the denominator is multiple of 10 we can directly convert the numerator into decimal according to the \[0's\]in the denominator. We can also convert the denominator into multiples of \[10\] by multiplying the numerator and denominator with the same number, it will make the fraction easier to convert into decimal form.