Answer:
The decimal number 0.16666... can be expressed as a fraction. To convert this decimal to a fraction, we can use the method of infinite geometric series.
Let's call the repeating decimal 0.16666... as x.
Multiply both sides of this equation by 10 to get rid of the decimal point:
10x = 1.66666...
Next, subtract the original equation from the one we just obtained to eliminate the repeating part:
10x - x = 1.66666... - 0.16666...
Simplifying this equation gives:
9x = 1.5
Now, divide both sides of the equation by 9 to solve for x:
x = 1.5/9
Simplifying further, we get:
x = 1/6
Therefore, the fraction equivalent of the decimal 0.16666... is 1/6.
Explanation:
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