Final answer:
To convert the repeating decimal 0.87 to a fraction, multiply by 100 to shift the decimal and then subtract the original number. This leaves you with 99x = 87, which simplifies to x = 87/99. Hence, the simplified fraction is 87/99 (Option B).
Step-by-step explanation:
To convert the repeating decimal 0.87, with 87 repeating indefinitely, to a simplified fraction, we can use algebra. Let's represent the repeating decimal as x:
x = 0.878787...
Multiply both sides of the equation by 100, since the repeating pattern is two digits long:
100x = 87.878787...
Now subtract the original x from this equation:
100x - x = 87.878787... - 0.878787...
99x = 87
Divide both sides by 99 to solve for x:
x = 87/99