How do you write -0.41overline 6 as a fraction?

Answer: \(-\frac{104}{249}\)

Explanation: To convert the repeating decimal \(-0.416\overline{16}\) into a fraction, we can use algebraic methods to isolate the repeating part. The repeating part is “16,” which helps us set up an equation to eliminate the decimal.

Steps:

1. Let \( x = -0.416161616...\).
2. To eliminate the repeating part, multiply \( x \) by 1000 (since the non-repeating part has three digits before the repeat):

1. Next, multiply \( x \) by 100 (to shift the decimal point two places to the right):

1. Now, subtract the second equation from the first:

1. Now, isolate \( x \):

1. The repeating decimal can be expressed as a fraction. The repeating part “16” contributes to the fraction:

1. Therefore, the final result is:

Thus, \(-0.416\overline{16}\) as a fraction is \(-\frac{104}{249}\).