Convert 0.14¯¯¯¯¯ to a fraction.(1 point) Responses 14101 Start Fraction 14 over 101 End Fraction 1499 Start Fraction 14 over 99 End Fraction 7500 Start Fraction 7 over 500 End Fraction 750

Answer 1

To convert \( 0.14\overline{14} \) (which means that the digits '14' repeat indefinitely) to a fraction, we can use the following steps:

Let \( x = 0.14141414... \)

To eliminate the repeating part, we can multiply \( x \) by 100 (since there are 2 digits in the repeating part):

\[ 100x = 14.141414... \]

Now, we can set up the following equation:

\[ 100x = 14 + x \]

Now, we subtract \( x \) from both sides:

\[ 100x - x = 14 \]

This simplifies to:

\[ 99x = 14 \]

Now, we can solve for \( x \):

\[ x = \frac{14}{99} \]

Thus, the fraction representation of \( 0.14\overline{14} \) is \( \frac{14}{99} \).

The answer is \( \frac{14}{99} \).