0.16667 Repeating as a Fraction
What is 0.16667 Repeating?
0.16667 repeating is a decimal number that has a repeating pattern of 6 and 7. It is a non-terminating decimal that goes on indefinitely in a repeating cycle. In other words, it is an infinite decimal that never ends.
Converting 0.16667 Repeating to a Fraction
To convert 0.16667 repeating to a fraction, we can use a few different methods. One way is to use the fact that the repeating pattern is 6 and 7, and that the number of digits in the repeating pattern is 2.
Let's call the repeating decimal x. Then, we can set up the following equation:
x = 0.16667...
Since the repeating pattern is 2 digits long, we can multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 16.6667...
Next, we can subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 16.6667... - 0.16667...
This simplifies to:
99x = 16.5
Finally, we can divide both sides of the equation by 99 to solve for x:
x = 16.5 / 99
x = 1/6
So, 0.16667 repeating as a fraction is equal to 1/6.
Alternative Methods
There are other ways to convert 0.16667 repeating to a fraction. One alternative method is to use the fact that the repeating decimal is equal to a geometric series.
Let's call the repeating decimal r. Then, we can write:
r = 0.16667...
r = 0.1 + 0.06 + 0.006 + 0.0006 + ...
This is a geometric series with first term a = 0.1 and common ratio r = 0.1. We can use the formula for the sum of an infinite geometric series to find the value of r:
r = a / (1 - r)
r = 0.1 / (1 - 0.1)
r = 0.1 / 0.9
r = 1/9
r = 1/6
So, using this alternative method, we again find that 0.16667 repeating as a fraction is equal to 1/6.
