0.1666... as a Fraction
The repeating decimal 0.1666... is a fascinating mathematical concept that can be expressed as a fraction. In this article, we will explore how to convert 0.1666... into a fraction and discuss some interesting properties of this fraction.
The Decimal Expansion
The decimal expansion of 0.1666... is an infinite sequence of repeating digits: 0.1666666666.... This sequence has no terminating point, and the digits continue to repeat indefinitely.
Converting 0.1666... to a Fraction
To convert 0.1666... to a fraction, we can use the following steps:
- Let x = 0.1666...
- Multiply both sides of the equation by 10 to get 10x = 1.666...
- Subtract x from both sides to get 9x = 1.5
- Divide both sides by 9 to get x = 1.5/9
- Simplify the fraction to get x = 1/6
The Fractional Form
Therefore, 0.1666... can be expressed as a fraction in its simplest form as:
1/6
Properties of the Fraction
The fraction 1/6 has some interesting properties:
- Recurring Decimal: As we've seen, the decimal expansion of 1/6 is a recurring decimal, 0.1666...
- Simplest Form: The fraction 1/6 is in its simplest form, meaning that it cannot be reduced further.
- Unit Fraction: 1/6 is a unit fraction, which means that it has a numerator of 1.
Conclusion
In conclusion, the repeating decimal 0.1666... can be expressed as a fraction in its simplest form as 1/6. This fraction has some fascinating properties, including its recurring decimal expansion and simplest form.
