0.063 Repeating as a Fraction
What is 0.063 Repeating?
0.063 repeating, also known as 0.063~, is a decimal number that has a repeating pattern of digits. In this case, the digits "063" repeat indefinitely. This type of decimal is also known as a recurring decimal or a repeating decimal.
Converting 0.063 Repeating to a Fraction
To convert 0.063 repeating to a fraction, we can use a few different methods. One way is to use the fact that the repeating part of the decimal (063) has a finite number of digits. Let's call this repeating part "r".
Let x = 0.063~
Since the repeating part has three digits, we can multiply both sides of the equation by 1000 to get:
1000x = 63.063~
Subtracting the original equation from this new equation, we get:
999x = 63
Dividing both sides by 999, we get:
x = 63/999
Simplifying this fraction, we get:
x = 7/111
Therefore, 0.063 repeating as a fraction is equal to 7/111.
Properties of the Fraction 7/111
The fraction 7/111 has some interesting properties. For example:
- It is a unit fraction, meaning that the numerator is 1 or the denominator is a factor of the numerator.
- It is an irreducible fraction, meaning that it cannot be simplified further.
- It has a denominator of 111, which is a Blum integer (a product of two prime numbers).
Conclusion
In conclusion, 0.063 repeating as a fraction is equal to 7/111. This fraction has some interesting properties, including being a unit fraction and an irreducible fraction. By using the methods described above, we can convert any repeating decimal to a fraction.
