Question

How do you convert 4.36 (36 being repeated) to a fraction?

Answer 1

Hint: Here in this question, we have to convert 4.36 to a fraction where 36 is a repetitive number. We will form two equations to solve this question. In the first question, we will let the number given as ‘x’. And the second equation will be formed by multiplying the whole equation with 100. After that both the equation will get subtracted and solved to get the answer.

Complete step by step answer:
Let’s discuss the question.
In this question, we will form a linear equation in one variable in which we will find the value of that variable. We will be assigning the given number by some variable.
As 36 is a number which is being repeated and it is a 2 digit number. In order to skip two decimal places we will multiply the whole equation by 100. So, in this case, two equations will be formed in total. In the first equation, we will assign the given number by ‘x’. It will become our first equation and the second equation will be formed when we will multiply the first equation by 100 on both sides. In this equation, the decimal of 4.36 will be skipped right and the decimal again will be placed 2 digits before. After decimal, 36 will be placed as it is a repetitive number. After all these steps, we will finally subtract both the equations to find the value of ‘x’ which will be in a fraction. So, let’s start to solve this question.
Let $x=4.36.....(i)$
Multiply the whole equation by 100. We will get:
$\Rightarrow 100\times x=100\times 4.36$
As we know that while multiplying with the 100, the decimal will shift to the right hand side up to 2 decimal places and 36 will come after the decimal because it is being repeated. Now we will get:
$\Rightarrow 100x=436.36.......(ii)$
Next step is to subtract equation(i) from equation(ii). We will get:
$\Rightarrow 100x-x=436.36-4.36$
On solving further we will get:
$\Rightarrow 99x=432$
Now solve to find x:
$\Rightarrow x=\dfrac{432}{99}$
On dividing, we will get:
$\therefore x=\dfrac{48}{11}$
So this is our final answer.

Note:
Note that on multiplying the number by 10, 100, 1000 and so on, the decimal will shift towards right and on dividing with the same numbers the decimal will get shifted to left. This is a very silly mistake which can be done by students. Another mistake is while conversion, students can convert by removing the decimal of 4.36 and placing 100 in the denominator and reducing it. This should not be done.