Question

The number \(0.4\overline{23}\) converted to a fraction, then it is equal to:

• A. \(\frac{1147}{300}\)
• B. \(\frac{419}{900}\)
• C. \(\frac{419}{990}\)
• D. \(\frac{423}{100}\)

Answer 1

The Correct Option is C

The decimal number \(0.4\overline{23}\) can be converted to a fraction by following these steps:

1. Let \(x = 0.4\overline{23}\). This means \(x = 0.4232323\ldots\)

2. Multiply both sides by \(1000\) to shift the decimal point past the repeating part: \(1000x = 423.232323\ldots\)

3. Again, multiply by \(10\) to shift the decimal to align with the repeating sequence: \(10x = 4.232323\ldots\)

4. Subtract the equation from step 3 from the equation in step 2:

\(1000x - 10x = 423.232323\ldots - 4.232323\ldots\)

5. Simplify the equations: \(990x = 419\)

6. Now, solve for \(x\) by dividing both sides by \(990\): \(x = \frac{419}{990}\)

Therefore, the fraction representation of \(0.4\overline{23}\) is \(\frac{419}{990}\).