0.16666 as a Fraction Simplified
The repeating decimal 0.16666 can be written as a fraction in its simplest form. But how do we do it?
Step 1: Write the Decimal as a Fraction
To convert 0.16666 to a fraction, we can write it as:
0.16666 = 16666/100000
Step 2: Simplify the Fraction
To simplify the fraction, we need to find the greatest common divisor (GCD) of 16666 and 100000.
Using the Euclidean algorithm or prime factorization, we find that the GCD is 2.
So, we can divide both the numerator and the denominator by 2:
16666 ÷ 2 = 8333 100000 ÷ 2 = 50000
This gives us:
0.16666 = 8333/50000
Step 3: Check for Further Simplification
To check if the fraction can be further simplified, we can look for common factors between 8333 and 50000.
Using the Euclidean algorithm again, we find that there are no common factors other than 1.
Therefore, the simplified fraction is:
0.16666 = 1/6
There you have it! The repeating decimal 0.16666 is equal to the simplified fraction 1/6.
