Question

What is $\left( {\dfrac{{20}}{{30}}} \right)$ as a decimal?

Answer 1

Hint: In the given question, we are required to convert a given fraction into decimal. The fraction is having numerator and denominator. So, we first simplify the fraction and bring it in simplest form. Then, we convert it into decimal directly by division. We continue the division process until we get remainder as zero.

Complete step-by-step solution:
The given question requires us to convert the given fraction into its simplest form by cancelling out the common factors in numerator and denominator and then expressing it as decimal representation.
So, to convert the given fraction into its simplest form, we factorise the numerator as well as denominator and look for the common factors.
We have, \[20 = 2 \times 2 \times 5\] and \[30 = 3 \times 2 \times 5\].
So, cancelling out the numerator and denominator by the common factor $2$ and $5$, we get,
\[\left( {\dfrac{{20}}{{30}}} \right) = \left( {\dfrac{{2 \times 10}}{{3 \times 10}}} \right) = \left( {\dfrac{2}{3}} \right)\]
Now, to convert the fraction into the decimal representation, we divide the numerator by the denominator until we get zero as the remainder.
We know that the numerator \[2\] is less than \[3\]. So, we place a decimal point first and carry a zero and continue the division.
Now, we have to divide $20$by $3$ after placing a decimal point. So, we get $6$ quotient and $2$ as remainder in this case. Similarly, we carry a zero again as we have placed a decimal point earlier. So, we have to again divide $20$by $3$. Hence, this division keeps repeating and we get a non terminating but recurring decimal representation for the fraction $\left( {\dfrac{{20}}{{30}}} \right)$.
Hence, we get, \[\left( {\dfrac{{20}}{{30}}} \right) = \left( {\dfrac{2}{3}} \right) = 0.6666....\]

Note: The division of the numerator by the denominator can be a cumbersome task as it involves thorough knowledge of algebraic rules and long division method. Care should be taken while doing the same and proceeding with the process to convert a fraction into decimal.