0.05 Repeating as a Fraction in Simplest Form
Introduction
When we encounter a repeating decimal, it can be challenging to convert it into a fraction. However, with the right steps, we can simplify the fraction to its simplest form. In this article, we will explore how to convert 0.05 repeating as a fraction in its simplest form.
Converting 0.05 Repeating to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
- Let x be the repeating decimal: In this case, let x = 0.050505...
- Multiply x by 10: 10x = 0.505050...
- Subtract x from 10x: 10x - x = 0.505050... - 0.050505...
- Simplify the equation: 9x = 0.45
- Divide by 9: x = 0.45/9
Now, let's perform the calculation:
x = 0.45/9 x = 5/90 x = 1/18
Simplest Form
The fraction 1/18 is already in its simplest form. We can verify this by checking if the numerator and denominator have any common factors. Since they don't, the fraction is in its simplest form.
Conclusion
In conclusion, the repeating decimal 0.05 can be converted to a fraction in its simplest form as 1/18. By following the steps outlined above, we can easily convert any repeating decimal to a fraction and simplify it to its simplest form.
