0.16666... as a Fraction
Introduction
The decimal number 0.16666... is a repeating decimal, where the sequence of digits "6" repeats indefinitely. You may wonder, what is the equivalent fraction of this decimal number? In this article, we will explore how to convert 0.16666... to a fraction.
The Formula
To convert a repeating decimal to a fraction, we can use the following formula:
x = decimal number y = number of digits in the repeating part z = number of non-repeating digits
The formula is:
frac(x - z) / (10^y - 1)
Converting 0.16666...
Let's apply the formula to our decimal number:
x = 0.16666... y = 1 (since the repeating part is only 1 digit, which is 6) z = 0 (since there are no non-repeating digits)
Plugging in the values, we get:
frac(x - 0) / (10^1 - 1) = frac(0.16666... - 0) / (10 - 1) = frac(0.16666...) / 9
Simplifying the Fraction
To simplify the fraction, we can multiply both the numerator and denominator by 6 to eliminate the decimal part:
= (6 * 0.16666...) / (9 * 6) = 1 / 9
The Result
Therefore, the equivalent fraction of 0.16666... is 1/9.
Conclusion
In this article, we have successfully converted the repeating decimal 0.16666... to a fraction using the formula. We hope this helps you understand the relationship between decimals and fractions better.
