.16667 Repeating as a Fraction
The decimal number .16667 is a repeating decimal, which means that it has a sequence of digits that repeats indefinitely. In this case, the repeating sequence is "1667". But have you ever wondered what this decimal represents as a fraction?
Converting .16667 to a Fraction
To convert .16667 to a fraction, we can use the following steps:
- Let x = .16667 This will be our starting point.
- Multiply both sides by 10,000 We get 10,000x = 1666.67
- Subtract x from both sides 10,000x - x = 1666.67 - 0.16667 9,999x = 1666.50
- Divide both sides by 9,999 x = 1666.50 / 9,999 x = 1/6
So, .16667 repeating is equal to the fraction 1/6.
Why Does This Work?
This method works because the repeating decimal .16667 can be thought of as an infinite geometric series:
.16667 = 1/10 + 6/10^2 + 6/10^3 + 7/10^4 + ...
When we multiply both sides by 10,000, we are essentially shifting the decimal place to the left, which allows us to cancel out the repeating pattern. By subtracting x from both sides, we eliminate the fractional part of the decimal, leaving us with a simple fraction.
Conclusion
In conclusion, the repeating decimal .16667 is equal to the fraction 1/6. This conversion is possible through a series of simple algebraic steps, which involve multiplying and dividing by powers of 10 to eliminate the repeating pattern.
