To find the value of [tex]\(45 - 0.023\)[/tex], we need to perform the subtraction operation step-by-step. Here we go:
1. Start with the value 45.
2. Subtract 0.023 from 45.
When you subtract 0.023 from 45:
[tex]\[ 45.000 - 0.023 \][/tex]
You need to align the decimal points and subtract each corresponding digit starting from the smallest place value (the thousandths place) to the largest:
[tex]\[
\begin{array}{r}
45.000 \\
- 0.023 \\
\hline
\end{array}
\][/tex]
- First, subtract the thousandths place: [tex]\(0 - 3\)[/tex] needs borrowing. Borrow from the hundredths place (making it 9 after borrowing) and thousandths place becomes 10. Now, [tex]\(10 - 3 = 7\)[/tex].
- Next, subtract the hundredths place: [tex]\(9 - 2 = 7\)[/tex].
- Then, subtract the tenths place: [tex]\(10 - 0 = 10\)[/tex], but we need to borrow from the tens place again so next operation becomes [tex]\(4 - 1 = 3\)[/tex].
- Lastly, subtract the units place: [tex]\(4 - 0 = 4\)[/tex].
Combining these results, we get:
[tex]\[ 45 - 0.023 = 44.977 \][/tex]
So, the value of [tex]\(45 - 0.023\)[/tex] is [tex]\(\boxed{44.977}\)[/tex].
This matches with the provided option B. So, the correct answer is:
B. 44.977
