Question

Convert 0.14--------- to a fraction.

Answer 1

To convert the repeating decimal \(0.14\overline{14}\) (which means the digits "14" repeat indefinitely) into a fraction, we can follow these steps:

1. Let \( x = 0.141414...\).

2. To eliminate the repeating part, multiply \( x \) by 100 (since the repeating part has two digits, we shift the decimal point two places to the right):
\[
100x = 14.141414...
\]

3. Now, we can set up an equation using both forms we have:
\[
100x = 14.141414... \quad (1)
\]
\[
x = 0.141414... \quad (2)
\]

4. Subtract equation (2) from equation (1):
\[
100x - x = 14.141414... - 0.141414...
\]
\[
99x = 14
\]

5. Solve for \( x \):
\[
x = \frac{14}{99}
\]

Thus, the repeating decimal \(0.14\overline{14}\) can be converted into the fraction \( \frac{14}{99} \).