Question

Write the rational number $\dfrac{7}{4}$ in decimal form.

Answer 1

Hint: In the given question, we are required to convert a given rational number into decimal form. The rational number has a numerator and denominator. So, we first simplify the rational number and bring it in simplest form by cancelling the common factors in numerator and denominator and in order to convert it into decimal we perform the division.

Complete step-by-step solution:
The given question requires us to convert the given rational number 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 rational number into its simplest form, we factorise the numerator as well as denominator and look for the common factors.
We have, $7 = 7 \times 1$ and $4 = 2 \times 2$.
There is no common factor between numerator and denominator. So, the rational number is in its simplest form already.
Now, to convert the rational number into the decimal representation, we divide the numerator by the denominator until we get zero as the remainder.
But, we know that division by any power of ten is easier as compared to division by any other number. So, we multiply the numerator and denominator by $25$ to get $100$ as the denominator.
So, we have, $\dfrac{7}{4} \times \dfrac{{25}}{{25}}$
Multiplying and simplifying the product, we get,
$= \dfrac{{175}}{{100}}$
Now, we know that division of any number by the power of ten is simple as we just have to shift the decimal point to the left of the same number of digits as the number of zeroes in the power of ten.
Hence, we get, $\dfrac{{175}}{{100}} = 1.75$.

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 rational number into decimal. Rational numbers either have a terminating decimal expansion or non-terminating but recurring decimal expansion.