2/5 as a Repeating Decimal
When we divide 2 by 5, we get a decimal result that may seem simple at first, but has some interesting properties. In this article, we'll explore what happens when we convert 2/5 to a decimal and why it becomes a repeating decimal.
What is 2/5 as a Decimal?
To convert 2/5 to a decimal, we can simply divide 2 by 5:
2 ÷ 5 = 0.4
At first glance, it seems like a simple decimal result. However, if we take a closer look, we'll notice that the decimal expansion of 2/5 is not as straightforward as it seems.
The Repeating Pattern
When we try to expand the decimal result of 2/5 further, we get:
0.4 = 0.40 = 0.400 = 0.4000 = ...
Notice a pattern? The digits "0" and "4" keep repeating in an infinite cycle. This is because 2/5 is a rational number, which means it can be expressed as a finite decimal or a ratio of integers. In this case, the ratio is 2:5, and the resulting decimal expansion is a repeating pattern of 0 and 4.
Why Does 2/5 Become a Repeating Decimal?
The reason why 2/5 becomes a repeating decimal is due to the way we perform long division. When we divide 2 by 5, we get a remainder of 2. To get a more accurate result, we can add more decimal places by multiplying the remainder by 10 and repeating the division process.
In the case of 2/5, the remainder is always 2, and when we multiply it by 10, we get 20. When we divide 20 by 5, we get 4 with a remainder of 0. This is why the decimal expansion of 2/5 starts with 0.4.
However, when we multiply the remainder of 0 by 10, we still get 0, and when we divide it by 5, we get 0 with a remainder of 0. This is why the decimal expansion of 2/5 starts to repeat itself.
Conclusion
In conclusion, 2/5 as a decimal is a repeating decimal that follows a pattern of 0 and 4. This is due to the way we perform long division and the fact that 2/5 is a rational number. Understanding why 2/5 becomes a repeating decimal can help us appreciate the intricacies of mathematics and the beauty of patterns in numbers.
