To convert the repeating decimal 0.477777... into a fraction, use the geometric series trick. The resulting fraction is 4.3/9 in its simplest form.
To convert the repeating decimal 0.477777... into a fraction, we can use a trick called geometric series. Let x = 0.477777..., then multiply both sides of the equation by 10 to get 10x = 4.777777... Subtracting the original equation from the second equation, we have 10x - x = 4.777777... - 0.477777..., which simplifies to 9x = 4.3.
Now, solve for x by dividing both sides of the equation by 9: x = 4.3/9. This can be further simplified by dividing the numerator and the denominator by their greatest common denominator (GCD), which is 1. The fraction 4.3/9 is already in its simplest form and cannot be simplified any further.
Learn more about Converting repeating decimals to fractions