Question

How do you change the given decimal 3.5 into a fraction?

Answer 1

Hint: We start solving the problem by equating the given decimal to a variable. We then make use of the fact that in order to convert the given decimal of form $a.bcd.....nplaces$ can be converted to fraction as $\dfrac{abcd......\left( n+1 \right)terms}{{{10}^{n}}}$ to proceed through the problem. We use this fact and then factorize the numerator and denominator to proceed further through the problem. We then make the necessary calculations to get the required fraction form of the given decimal.

Complete step by step answer:
According to the problem, we are asked to convert the given decimal 3.5 into a fraction.
Let us assume d = 3.5 ---(1).
We know that in order to convert the given decimal of the form $a.bcd.....nplaces$ can be converted to fraction as $\dfrac{abcd......\left( n+1 \right)terms}{{{10}^{n}}}$. Let us use this result to the decimal in equation (1).
So, we have $d=\dfrac{35}{10}$ ---(2).
Let us factorize the numbers present in the numerator and denominator of equation (2).
So, we get $35=5\times 7$, $10=5\times 2$. Let us use these results in equation (2).
$\Rightarrow d=\dfrac{5\times 7}{5\times 2}$ ---(3).
Let us cancel the common factors present in both numerator and denominator in equation (3).
$\Rightarrow d=\dfrac{7}{2}$.
So, we have found the fraction form of the given decimal 3.5 as $\dfrac{7}{2}$.
$\therefore $ The conversion of given decimal 3.5 to fraction is $\dfrac{7}{2}$.

Note:
We should perform each step carefully in order to avoid confusion and calculation mistakes while solving this problem. We can also solve this problem by multiplying and dividing the given fraction to get the required answer. Similarly, we can expect the problems to convert the given decimal 254.5735 to the fraction form.