Question

How do you convert 0.23 ( 23 being repeated ) to a fraction ?

Answer 1

Hint: According to the given question we need to convert the repeating rational number \[0.23\] (23 being repeated). We can say that 0.23 is a rational number because the number \[0.23\]. Can be expressed in the form of \[\dfrac{p}{q}\]. As we know that to remove the decimal or to shift the decimal to the right hand side to make it a whole number we multiply the number with putting the zeroes in the denominator and numerator by looking at the numbers after the decimal place. Therefore, \[0.23\] can be expressed as the fraction \[\dfrac{{23}}{{100}}\] that means it is definitely a rational number.

Complete Step by step answer:
In order to convert the number to fraction while it has repeating parts also. We first consider the number \[0.23\] and assume it to be x.
\[ \Rightarrow x = 0.23\]
Since, it is given in the question that in \[0.23\], 23 is being repeated and it makes up the 2 decimal places that means we need to multiply it by 100. This is the equation which comes up after multiplying.
\[ \Rightarrow 100x = 23.23\]
Moving further we are going to subtract \[x = 0.23\] having this value from both the sides, we are going to get somewhat this equation,
\[ \Rightarrow 100x - x = 23.23 - 0.23\]
\[ \Rightarrow 99x = 23\]
At last, to find the value of x we will make the coefficient of x as 1. For this we need to divide it by 99, we will get -
\[ \Rightarrow x = \dfrac{{23}}{{99}}\]
This is the required answer.

Note: Be careful while converting the decimal into a fraction. For doing this your first step should be to write the decimal in the form of fraction, that is every number can be written in the form of fraction as there is hidden 1 in the denominator. Then you should multiply both the numerator and denominator by 10 for every number after the decimal point. The last thing is to keep the simplified version as your answer.