To convert the repeating decimal 0.1666… (where the 6 repeats indefinitely) into a fraction, we can use a simple algebraic method.
Let x = 0.1666…
To eliminate the repeating part, we can multiply both sides of this equation by 10 (which moves the decimal point one space to the right):
10x = 1.666…
Now we have two equations:
- x = 0.1666…
- 10x = 1.666…
Next, we subtract the first equation from the second:
10x – x = 1.666… – 0.1666…
This simplifies to:
9x = 1.5
Now, to solve for x, divide both sides by 9:
x = 1.5 / 9
To simplify this fraction, we can convert 1.5 into a fraction itself:
1.5 = 3/2
Now substituting back, we get:
x = (3/2) / 9
This simplifies to:
x = 3/18
And finally, simplifying 3/18, we find:
x = 1/6
Therefore, the repeating decimal 0.1666… is equal to the fraction 1/6.