Question

How do you convert 0.12 (2 being repeated) to a fraction?

Answer 1

Hint: When we divide a decimal number then the number of zero will be equal to the number of digits after the decimal. For example, $\dfrac{{0.7}}{{10}},\dfrac{{0.77}}{{100}}$ and so on. Also, when we divide any number by 100 or 1000 then we will put the decimal point in the numerator.

Complete step by step solution:
Firstly, we will assume 0.12 be x, we get,
$ \Rightarrow x = 0.12$
Let this equation be (i)
It is given in the problem statement that 0.12 is repeating after 2 decimal places each which means we have to multiply it by 10. Multiply 10 on both sides of the equation (i)
 $ \Rightarrow 10x = 1.22$
Let this equation be (ii)
Now, we will subtract equation (i) from (ii), we get,
 $ \Rightarrow 10x - x = 1.22 - 0.12$
After solving the above equation, we get,
 $ \Rightarrow 9x = 1.1$
Now, we will divide both the sides with 9 so we get x as a fraction
$ \Rightarrow \dfrac{{9x}}{9} = \dfrac{{1.1}}{9}$
After simplifying the above equation, we get,
 $ \Rightarrow x = \dfrac{{1.1}}{9}$
Now, we will remove the decimal point in the numerator. So, to remove it we will add zeroes in the denominator and the zeroes will be according to the digits present after the decimal point, we get,
 $ \Rightarrow x = \dfrac{{11}}{{90}}$

Therefore, the fraction form of 0.12 is $\dfrac{{11}}{{90}}$.

Additional Information:
A decimal number has two parts; a whole number and a fractional part which is separated by a decimal point. The digit after the decimal point is smaller in value than the whole number of the same digit.

Note: A fraction represents part of a whole number. Whenever we solve a fraction ultimately the result will be in decimal form. To denote fractional part in a whole number we use decimal.
Also remember, a repeating decimal is also known as a recurring decimal. The problem which was stated above was a recurring decimal. For example,
$ \Rightarrow 0.5555 = 0.\overline {55} $
The line above 0.55 is known as a bar, it is also represented in this form.