Answer

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**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.

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