To write 0.666666 as a fraction, we can start by recognizing that the decimal number 0.666666 repeats indefinitely. This is because the digit 6 repeats infinitely after the decimal point. Let’s call this repeating decimal x.
To convert x into a fraction, we can use a basic algebraic method. Let’s multiply x by a power of 10 to eliminate the repeating part. Since there is only one digit after the decimal point, we can multiply x by 10 to get rid of the repeating part.
10x = 6.666666…
Now, we subtract the original equation from the one above to eliminate the repeating part:
10x – x = 6.666666… – 0.666666…
Simplifying the right side gives us:
9x = 6
Dividing both sides of the equation by 9 yields:
X = 6/9
Therefore, the repeating decimal 0.666666 can be written as the fraction 6/9.
It is important to note that we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 3 in this case.
Dividing 6 and 9 by 3, we get:
6 ÷ 3 / 9 ÷ 3 = 2/3
So, the simplified fraction form of 0.666666 is 2/3.
I hope this explanation helps clarify the process of converting a repeating decimal into a fraction. If you have any further questions, feel free to ask!