0.1 Repeating as a Simplified Fraction
What is 0.1 Repeating?
0.1 repeating, also known as 0.1̄, is a decimal number that has a repeating pattern of 1s after the decimal point. It can be written as:
0.1, 0.11, 0.111, 0.1111, ...
Converting 0.1 Repeating to a Simplified Fraction
To convert 0.1 repeating to a simplified fraction, we can use the following steps:
Step 1: Let x = 0.1 Repeating
Let's let x equal 0.1 repeating.
x = 0.1̄
Step 2: Multiply Both Sides by 10
Multiply both sides of the equation by 10.
10x = 1.1̄
Step 3: Subtract the Original Equation from the New Equation
Subtract the original equation from the new equation.
10x - x = 1.1̄ - 0.1̄
This simplifies to:
9x = 1
Step 4: Divide Both Sides by 9
Divide both sides of the equation by 9.
x = 1/9
Simplified Fraction
Therefore, 0.1 repeating can be written as a simplified fraction:
0.1̄ = 1/9
This means that the decimal 0.1 repeating is equal to the fraction 1/9.
