Final answer:
To convert the repeating decimal 0.673(7 and 3 being repeated) to a fraction, multiply both sides of the equation by 100 to eliminate the repeating part, subtract the original equation from the new equation, and simplify to find the fraction form of the repeating decimal.
Step-by-step explanation:
To convert the repeating decimal 0.673(7 and 3 being repeated) to a fraction, we can use the concept of geometric series. Let x = 0.67373737... Then, we multiply both sides of the equation by 100 to eliminate the repeating part:
100x = 67.373737...
Now, we subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 67.373737... - 0.67373737...
Simplifying this equation, we get:
99x = 66.7
Dividing both sides by 99 gives us the fraction form of the repeating decimal:
x = 66.7/99 = 2/3