0.1 Repeating as a Fraction in Simplest Form
What is 0.1 Repeating?
0.1 repeating, also known as 0.1̄, is a decimal number that has a repeating pattern of 1's after the decimal point. It can be written as 0.111111... where the 1's go on indefinitely.
Converting 0.1 Repeating to a Fraction
To convert 0.1 repeating to a fraction, we can use the following steps:
Let x = 0.111... (where x is the repeating decimal)
Multiply both sides by 10 to get:
10x = 1.111...
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 in simplest form is:
1/9
Why is 1/9 the Simplest Form?
The fraction 1/9 is in simplest form because it has no common factors between the numerator (1) and the denominator (9). In other words, 1 and 9 are coprime, meaning they do not share any common factors except for 1.
Conclusion
In conclusion, 0.1 repeating as a fraction in simplest form is 1/9. This conversion is useful in various mathematical applications, such as algebra, geometry, and calculus.
