0.05 Recurring as a Fraction
Have you ever stumbled upon a recurring decimal like 0.05 and wondered how to convert it into a fraction? You're not alone! In this article, we'll show you how to convert 0.05 recurring into a fraction.
What is a Recurring Decimal?
A recurring decimal, also known as a repeating decimal, is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.05 is a recurring decimal because the "05" sequence repeats indefinitely: 0.0505050505...
Converting 0.05 Recurring into a Fraction
To convert 0.05 recurring into a fraction, we can use the following steps:
Step 1: Let x = 0.0505...
Let's assume that x = 0.0505... (the recurring decimal 0.05).
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 5.0505...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation:
100x - x = 5.0505... - 0.0505...
This simplifies to:
99x = 5
Step 4: Divide by 99
Divide both sides of the equation by 99:
x = 5/99
Conclusion
And there you have it! The recurring decimal 0.05 can be converted into the fraction 5/99. This fraction represents the same value as the original recurring decimal.
Why is this Conversion Important?
Converting recurring decimals into fractions is important because fractions are often easier to work with in mathematical calculations. Additionally, fractions can help to reveal underlying patterns and relationships that may not be immediately apparent from the decimal form.
So the next time you encounter a recurring decimal, remember that you can convert it into a fraction using these simple steps!
