5/6 as a Repeating Decimal
When we divide 5 by 6, we get a result that seems to go on forever. This is because 5/6 is a fraction that cannot be expressed as a finite decimal. Instead, it becomes a repeating decimal.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, the decimal representation of 1/3 is 0.33333..., where the sequence "3" repeats forever.
5/6 as a Repeating Decimal
So, what is 5/6 as a repeating decimal? To find out, we can perform the division:
_______
6 | 5.0000
- 4
------
10
- 6
------
40
-36
------
40
-36
------
.
.
.
As we can see, the sequence 83 repeats indefinitely. Therefore, 5/6 as a repeating decimal is:
0.8333...
Properties of 5/6 as a Repeating Decimal
One interesting property of 5/6 as a repeating decimal is that it has a period of 2. This means that the sequence "83" repeats every two digits. This period is a characteristic of all repeating decimals.
Another property of 5/6 as a repeating decimal is that it is a non-terminating decimal. This means that it cannot be expressed as a finite decimal. Instead, it goes on forever.
Conclusion
In conclusion, 5/6 as a repeating decimal is 0.8333..., where the sequence "83" repeats indefinitely. This repeating decimal has a period of 2 and is a non-terminating decimal. Repeating decimals like 5/6 are an important part of mathematics, and understanding their properties can help us better understand the world around us.
