0.15 Recurring as a Fraction in Simplest Form
What is 0.15 Recurring?
0.15 recurring, also known as 0.151515..., is a decimal number that has a repeating pattern of 15. This type of decimal is called a recurring decimal or a repeating decimal.
Converting 0.15 Recurring to a Fraction
To convert 0.15 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.1515...
Let's assume that x = 0.1515...
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get:
100x = 15.1515...
Step 3: Subtract the original equation from the new equation
Subtract the original equation from the new equation:
100x - x = 15.1515... - 0.1515...
This simplifies to:
99x = 15
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 15/99
Step 5: Simplify the fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
x = 5/33
Therefore, 0.15 recurring as a fraction in simplest form is 5/33.
Conclusion
In conclusion, 0.15 recurring can be converted to a fraction in simplest form by following the steps outlined above. The result is 5/33, a simple fraction that represents the recurring decimal 0.15.
