Question

How do you convert 0.47(47 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 0.47. It is mentioned that 47 is repeated after the decimal point.

Hence, we can say that 0.47 is a repeating decimal number. Here repeating decimal number can be represented as:\[0.\overline {47} \].

A bar is added above 47 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,\[0.\overline {47} \] is repeating as a fraction we get
\[
\dfrac{{(0.47 \times 100) - 0}}{{99}} \\
= \dfrac{{47}}{{99}} \\
\]
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.