0.15 Repeating as a Decimal
What is 0.15 Repeating?
0.15 repeating, also written as 0.15̄, is a decimal representation of a fraction where the digits "15" repeat indefinitely. This means that the decimal expansion goes on forever and ever, with the same sequence of digits "15" repeating over and over again.
Conversion to Fraction
To convert 0.15 repeating to a fraction, we can use the following formula:
Let x = 0.151515...
Multiply both sides by 100 to get rid of the decimal point:
100x = 15.1515...
Subtract x from both sides to get:
99x = 15
Divide both sides by 99:
x = 15/99
x = 5/33
So, 0.15 repeating is equal to the fraction 5/33.
Properties of 0.15 Repeating
Here are some interesting properties of 0.15 repeating:
Rational Number
0.15 repeating is a rational number, which means it can be expressed as a finite decimal or a ratio of integers (in this case, 5/33).
Non-Terminating, Non-Repeating
Although the digits "15" repeat, the decimal expansion of 0.15 repeating goes on indefinitely and never terminates.
** Irrational Square Root**
The square root of 0.15 repeating is an irrational number, which cannot be expressed as a finite decimal or a ratio of integers.
Applications
0.15 repeating appears in various mathematical concepts, such as geometry, algebra, and calculus. It is also used in real-world applications, like finance, engineering, and computer science.
Conclusion
In conclusion, 0.15 repeating is an interesting and important decimal that has many unique properties and applications. By understanding its conversion to a fraction, properties, and uses, we can gain a deeper appreciation for the beauty and complexity of mathematics.
