Question

How do you convert 0.51(51 being repeated) to a fraction?

Answer 1

Hint: In the above given question we have to convert the decimal number with the same numbers repeated after it into fraction. We can do this by using a formula to convert from decimal to fraction in which of repeated number size should be known.

Complete step-by-step solution:
Given is the decimal fraction that is 0.51. It is mentioned that 51 is repeated after the decimal point. Hence, we can say that 0.51 is a repeating decimal number. Here repeating decimal numbers can be represented as:\[0.\overline {51} \].

A bar is added above 51 since both the numbers are repeated. For example, if only 7 was repeated then the bar would have only been on 7 denoting that only 7 is repeating.
The formula for converting the repeated decimal number to fraction is given below:
\[\dfrac{{(DN \times F) - NRP}}{D}\]
where DN stands for decimal number.
F stands 100 if repeating number is of size 2
NRP stands for Non-repeating part of decimal number.
D is 99 if the repeating number is of size 2.
Therefore, by substituting the values we get,
Since,\[0.\overline {51} \] is repeating as a fraction we get
\[
  \dfrac{{(0.51 \times 100) - 0}}{{99}} \\
   = \dfrac{{51}}{{99}} \\
 \]

Hence, we get the above answer in the form of fraction.

Note: An important part to note is that the non-repeating number here is 0 because it is the only number which is not repeating. For example, if only 7 was repeating after the decimal point then the non-repeating part from 0.47 will be 0.4.