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 \( \frac{13}{90} \).