1. The problem asks for the value of the digit 3 in the number 12.638. 2. In a decimal number, digits to the right of the decimal point represent fractional parts: tenths, hundredths, thousandths, etc. 3. The first digit after the decimal is tenths ($10^{-1}$), the second is hundredths ($10^{-2}$), and the third is thousandths ($10^{-3}$). 4. In 12.638, the digit 3 is in the hundredths place. 5. Therefore, the value of the digit 3 is $3 \times 10^{-2} = 0.03$. 6. So, the digit 3 represents three hundredths or 0.03 in the number 12.638.