Question

What is $1.5$ repeated as a fraction?

Answer 1

Hint: From the above question we have to convert the $1.5$ repeated into a fraction. Here $1.5$ repeated can be written as$1.\bar{5}$, to convert into a fraction first we have to assume a variable let “x” is the given decimal then we have to multiply both sides with $10$ and$100$, after that we have to subtract the$100x-10x$, from this we will get the variable “x” in a fraction form.

Complete step by step solution:
From the above question we have to convert given decimal into fraction, the given decimal is,
$\Rightarrow 1.5\left( repeating \right)$
As we know that it can be written as
$\Rightarrow 1.5\left( repeating \right)=1.55555\ldots =1.\bar{5}$
Now we have to assume that the variable “x” is equal to the given decimal that is,
$\Rightarrow x=1.\bar{5}$
First, we have to multiply both sides with $10$,
By multiplying we will get,
$\Rightarrow 10x=15.\bar{5}$
Now we have to multiply both sides with $100$,
By multiplying we will get,
$\Rightarrow 100x=155.\bar{5}$
Now we have to subtract the $10x$ from $100x$, that is,
$\Rightarrow 100x-10x$
By doing subtraction we will get,
$\Rightarrow 100x-10x=155.\bar{5}-15.\bar{5}$
By further simplification we will get,
$\Rightarrow 90x=140.0$
Now we have shift the $90$ from left hand side to the right-hand side,
By shifting $90$ from left hand side to the right-hand side, we will get,
$\Rightarrow x=\dfrac{140}{90}$
By further simplification we will get,
$\Rightarrow x=\dfrac{14}{9}$

Therefore, the conversion of $1.\bar{5}$ into a fraction is $\dfrac{14}{9}$.

Note: Students should know the conversion of decimals into the fraction, if in the question there is no repeated term means students can write directly $1.5$ as $\dfrac{15}{10}$ then we can do further simplification to get simplified fraction.