write 0.41 repeated indefinitely as a fraction

1 answer

To write 0.41 repeated indefinitely as a fraction, we will use algebraic manipulation. Let's denote the repeating decimal as x:
x = 0.414141...

Multiply both sides of the equation by 100 to remove the decimal point:
100x = 41.414141...

Subtract the two equations:
100x - x = 41.414141... - 0.414141...
99x = 41

Now, divide both sides of the equation by 99 to solve for x:
x = 41/99

Therefore, 0.41 repeated indefinitely is equal to the fraction 41/99.