To solve the subtraction problem [tex]\(78.65 - 3.4279\)[/tex], follow these detailed steps:
1. Align the Decimal Points: Start by writing the numbers vertically and aligning the decimal points.
```
78.6500
- 3.4279
```
2. Subtract Digit by Digit: Begin subtracting from the rightmost digit.
- Subtract the thousandths place:
[tex]\(0 - 9\)[/tex] is not possible, so we need to borrow from the hundredths place.
Borrowing reduces the hundredths place from [tex]\(0\)[/tex] to [tex]\(-1\)[/tex].
- Subtract the ten-thousandths place:
Before borrowing, it would be [tex]\(0 - 7\)[/tex], not possible. Continue to borrow until you get sufficient value.
As we borrow step by step, here are the steps followed through the digits:
```
Original:
78.6500
- 3.4279
```
After borrowing:
```
78.64910
- 3.4279
--> Becomes:
78.6500 (with adjustments)
```
3. Perform the subtraction:
- From the rightmost digits:
[tex]\(9 \from 10\)[/tex] (1 borrowed), we get [tex]\(1\)[/tex]
- Next place digits:
[tex]\(0 inherent \)[/tex]
- Move left:
Post borrowings through the digits:
4. Having done borrowings, note final subtraction values:
- Thousandths place: [tex]\(10 - 9 = 1\)[/tex]
- Hundredths place: [tex]\(9 - 2 = 7\)[/tex]
- Tenths place: [tex]\(4 - 3 = 1\)[/tex]
- Units place: [tex]\(8 - 0 : 8\)[/tex]
- Tens place: [tex]\(7 - 0 : 7\)[/tex]
5. Compile subtraction values aligned with initial borrowing:
```
75.22210000000001
```
Thus, the final result of [tex]\(78.65 - 3.4279\)[/tex] is [tex]\(\boxed{75.2221}\)[/tex], following through the straightforward subtraction process informed via alignment, borrowing adjustment.
