Question

How do you write a decimal with a repeating bar over it?

Answer 1

Hint: This question is from the topic of real numbers. In this question, we will understand how to write any decimal having a repeating bar over it. In solving this question, we will first understand using the examples. We will take such types of examples that have decimal as well as repeating bars.

Complete step by step solution:
Let us solve this question.
In this question, we have asked how do we write a decimal with repeating bars over that decimal number.
Let us first understand what a number is called which is having decimal and repeating bars over it. We call that number a repeating decimal or recurring decimal. The repeating decimal is the decimal representation of a number whose digits are repeating at regular intervals (or we can say periodic) and the infinitely repeated portion is not zero.
Let us take some examples.
Let us take a number as \[\dfrac{1}{3}\]. This can be written as 0.3333.....
Here, we can see in the number 0.3333..... that after the decimal the number 3 is repeating infinite times.
So, we can write this as
\[\dfrac{1}{3}=0.3333......=0.\overline{3}\]
So, in the number \[0.\overline{3}\], we can see that it is a decimal with repeating bars over it.
Let us take another example.
The number \[\dfrac{3227}{555}\] can also be written as \[\dfrac{3227}{555}=5.8144144144......\]
We can write \[5.8144144144......\] as \[5.8\overline{144}\].
Here, the number 144 is repeating infinite times, that’s why we have placed a bar over it.

Note: We should have a better knowledge in the topic of real numbers to solve this type of question easily. We should know about decimal numbers. We should know about repeating bars. We can write a decimal number with repeating bar over it also in the following way:
\[\dfrac{5}{74}=0.0\overline{675}\]
Here, after the decimal, there is zero and after that 675 is repeating many times.