1. The problem asks for the place value of the digit 4 in the number 12.34. 2. Place value depends on the position of the digit relative to the decimal point. 3. Digits to the left of the decimal point represent units, tens, hundreds, etc., increasing by powers of 10. 4. Digits to the right of the decimal point represent tenths, hundredths, thousandths, etc., decreasing by powers of 10. 5. In the number 12.34, the digit 4 is in the second position to the right of the decimal point. 6. This position corresponds to the hundredths place, which is $10^{-2}$. 7. Therefore, the place value of 4 is calculated as: $$4 \times 10^{-2} = 4 \times 0.01 = 0.04$$ 8. So, the place value of 4 in 12.34 is 0.04.