To evaluate the expression [tex]\( 4.12 - 0.22 \)[/tex], follow these detailed steps:
1. Write the numbers in a column format, aligning the decimal points:
[tex]\[
\begin{array}{r}
4.12 \\
- 0.22 \\
\hline
\end{array}
\][/tex]
2. Subtract the numbers starting from the rightmost digit (hundredths place):
[tex]\[
\begin{array}{r}
4.12 \\
- 0.22 \\
\hline
3.90
\end{array}
\][/tex]
3. In the hundredths place: Subtract [tex]\(2\)[/tex] from [tex]\(2\)[/tex]. This gives [tex]\(0\)[/tex].
4. In the tenths place: Subtract [tex]\(2\)[/tex] from [tex]\(1\)[/tex]. Since you cannot subtract [tex]\(2\)[/tex] from [tex]\(1\)[/tex] directly, you need to borrow [tex]\(1\)[/tex] from the ones place. This makes the [tex]\(1\)[/tex] in the tenths place [tex]\(11\)[/tex] (after borrowing 1 from the ones place, which becomes 3). Now, subtract [tex]\(2\)[/tex] from [tex]\(11\)[/tex], which gives [tex]\(9\)[/tex].
5. In the ones place: Subtract [tex]\(0\)[/tex] from [tex]\(3\)[/tex], resulting in [tex]\(3\)[/tex].
Put together, following the alignment:
[tex]\[
4.12 - 0.22 = 3.90
\][/tex]
Therefore, the final result of [tex]\( 4.12 - 0.22 \)[/tex] is [tex]\( 3.9 \)[/tex].
