0.1 Repeating as a Fraction
What is 0.1 Repeating?
0.1 repeating, also known as 0.1̄, is a decimal number that has a never-ending sequence of 1s after the decimal point. It is a non-terminating, repeating decimal. In other words, it is a decimal number that goes on forever without terminating.
Converting 0.1 Repeating to a Fraction
To convert 0.1 repeating to a fraction, we can use the following method:
Let x = 0.1̄
Multiply both sides by 10 to get:
10x = 1.1̄
Subtract x from both sides to get:
9x = 1
Divide both sides by 9 to get:
x = 1/9
So, 0.1 repeating as a fraction is equal to 1/9.
Simplifying the Fraction
The fraction 1/9 is already in its simplest form, so we don't need to simplify it further.
Conclusion
In conclusion, 0.1 repeating as a fraction is equal to 1/9. This conversion is useful in various mathematical calculations and applications. Understanding how to convert repeating decimals to fractions is an essential skill in mathematics, and this conversion is a great example of that.
