0.15 Repeating as a Fraction in its Simplest Form
What is 0.15 Repeating?
0.15 repeating, also known as 0.151515..., is a decimal number that repeats indefinitely in a cycle of 15. This type of number is called a repeating decimal or a recurring decimal.
Converting 0.15 Repeating to a Fraction
To convert 0.15 repeating to a fraction, we can use the following steps:
Let x = 0.151515...
Multiply both sides by 100 to get:
100x = 15.151515...
Now, subtract x from both sides to get:
99x = 15
Divide both sides by 99 to get:
x = 15/99
Simplifying the Fraction
The fraction 15/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
x = (15 ÷ 3) / (99 ÷ 3) = 5/33
Therefore, 0.15 repeating as a fraction in its simplest form is 5/33.
Conclusion
In conclusion, 0.15 repeating can be converted to a fraction in its simplest form by following the steps outlined above. The result is a simple fraction, 5/33, which is easy to work with in mathematical calculations.
