0.26 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we'll explore how to convert 0.26 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.26 repeating is a repeating decimal because the sequence "26" repeats indefinitely.
Converting 0.26 Repeating into a Fraction
To convert 0.26 repeating into a fraction, we can use the following steps:
Step 1: Identify the Repeating Part
The repeating part of the decimal is "26".
Step 2: Set Up the Equation
Let's set up an equation to convert the repeating decimal into a fraction. Let x = 0.2626... (where the dots represent the repeating sequence).
Step 3: Multiply Both Sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 26.2626...
Step 4: Subtract the Original Equation
Subtract the original equation from the new equation to eliminate the repeating part.
100x - x = 26.2626... - 0.2626...
This simplifies to:
99x = 26
Step 5: Solve for x
Divide both sides of the equation by 99 to solve for x.
x = 26/99
Therefore, 0.26 repeating as a fraction is 26/99.
Conclusion
In conclusion, converting a repeating decimal into a fraction involves identifying the repeating part, setting up an equation, and solving for the fraction. By following these steps, we can convert 0.26 repeating into the fraction 26/99.
