Question

tell me simple steps to Convert 0.14¯¯¯¯¯ to a fraction.

Answer 1

To convert the repeating decimal \( 0.14\overline{4} \) (which means 0.144444...) to a fraction, follow these simple steps:

1. **Set up an equation**: Let \( x = 0.14\overline{4} \).

2. **Multiply by a power of 10**: Since the repeating part (4) has one digit, multiply by 10 to shift the decimal point one place to the right:
\[
10x = 1.44444\ldots
\]

3. **Multiply by another power of 10 to isolate the repeating part**: Now, multiply \( x \) by 100 (two places since there are two digits before the repeating part):
\[
100x = 14.44444\ldots
\]

4. **Subtract the two equations**: Now you have:
\[
100x - 10x = 14.44444\ldots - 1.44444\ldots
\]
Simplifying this gives:
\[
90x = 13
\]

5. **Solve for \( x \)**:
\[
x = \frac{13}{90}
\]

Thus, the repeating decimal \( 0.14\overline{4} \) can be expressed as the fraction \( \frac{13}{90} \).