0.1 1 Repeating as a Simplified Fraction
Have you ever wondered how to convert a repeating decimal into a simplified fraction? In this article, we'll explore how to convert 0.1 1 repeating into a simplified fraction.
Understanding Repeating Decimals
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.1 1 repeating, the sequence of digits is "1" repeating indefinitely. To convert this repeating decimal into a simplified fraction, we need to find the equivalent fraction that has the same value.
Method to Convert Repeating Decimals into Fractions
There are several methods to convert repeating decimals into fractions, but one of the most common methods is to use the following formula:
x = decimal number n = number of digits in the repeating sequence
Step 1: Multiply both sides of the equation by 10^n.
Step 2: Subtract the original equation from the new equation.
Step 3: Simplify the resulting fraction.
Converting 0.1 1 Repeating into a Simplified Fraction
Let's apply the above method to convert 0.1 1 repeating into a simplified fraction.
Step 1: Multiply both sides of the equation by 10^2 (since the repeating sequence has 2 digits).
10^2 * x = 10^2 * 0.1 1
100x = 11.11...
Step 2: Subtract the original equation from the new equation.
100x - x = 11.11... - 0.1 1
99x = 11
Step 3: Simplify the resulting fraction.
x = 11/99
Simplified Fraction
Therefore, the simplified fraction equivalent to 0.1 1 repeating is 11/99.
In conclusion, converting a repeating decimal into a simplified fraction involves using a simple formula and following a few steps. By applying this method, we can convert 0.1 1 repeating into a simplified fraction, which is 11/99.
