The number 0.423 converted to a fraction, then it is equal to:

The correct answer is Option (3) → \(\displaystyle\frac{419}{990}\)

Only the digits 23 repeat, so multiply by two powers of ten that line up the repeating part, and subtract to remove it.

• \(x=0.4232323\ldots\)

• \(1000x=423.2323\ldots\)        (1)

• \(10x=4.2323\ldots\)        (2)

• Subtracting (2) from (1), the repeating part cancels: \(990x=419\)

• \(x=\displaystyle\frac{419}{990}\)

Shortcut:

• Numerator: the number formed by all the digits minus the digits before the bar, \(423-4=419\).

• Denominator: a 9 for each repeating digit and a 0 for each non-repeating digit after the point, 990.