Final answer:
To express the repeating decimal 0.941941... as a fraction in simplest form, we represent it as 'x', multiply by 1000 to create a new equation (1000x), subtract the original 'x', and find x = 941/999, which is already in its simplest form as there is no common divisor greater than 1 between 941 and 999.
Step-by-step explanation:
To convert the repeating decimal 0.941941... to fraction form, we use algebraic manipulation. Let x represent the repeating decimal.
x = 0.941941...
To remove the decimal part, we multiply by a power of 10 thawhichuals the number of digits in the repeating part. In this case, it is 1000x since there are three repeating digits (941).
1000x = 941.941941...
We then subtract the original equation from this to eliminate the repeating part.
1000x - x = 941.941941... - 0.941941...
999x = 941
Now, we divide by 999 to solve for x.
x = 941 / 999
This fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator, but in this case, 941 and 999 do not have a common divisor greater than 1, so x = 941 / 999 is the fraction in simplest form.