To simplify the expression [tex]\(4.156 - 0.34\)[/tex], follow these steps:
1. Align the decimal points to ensure the numbers are correctly positioned for subtraction:
[tex]\[
\begin{array}{r}
4.156 \\
-0.340 \\
\end{array}
\][/tex]
2. Subtract the smallest decimal place first:
- Units up to thousandths place:
[tex]\[
6 - 0 = 6
\][/tex]
3. Move to the next decimal place:
- Units up to hundredths place:
[tex]\[
5 - 4 = 1
\][/tex]
4. Continue with the tenths place:
- Units up to tenths place:
[tex]\[
1 - 3 = 8 \quad \text{(note: we carry over 1 from the next decimal place)}
\][/tex]
5. Finally, subtract the whole numbers:
- Units up to the ones place:
[tex]\[
4 - 0 = 4
\][/tex]
After performing the subtraction, the result is:
[tex]\[
4.156 - 0.34 = 3.816
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{3.816}
\][/tex]
