To find the sum of the numbers \(2.48\), \(3.465\), \(701.532\), and \(102.1\), you can follow these steps:
1. Arrange the Numbers Vertically:
- Align the decimal points of all the numbers in a column format.
```
2.480
+3.465
701.532
+102.100
```
2. Add the Hundredths Place:
- Start with the farthest right digit (the thousandths place if present):
- For the hundredths place:
- 0 (in 2.480) + 5 (in 3.465) + 2 (in 701.532) + 0 (in 102.100) = 7
- Write down 7 in the hundredths place.
3. Add the Tenths Place:
- Move to the tenths place:
- 8 (in 2.480) + 6 (in 3.465) + 3 (in 701.532) + 1 (in 102.100) = 18
- Write down 8 in the tenths place and carry over 1 to the units place.
4. Add the Units Place:
- Add the units place, including any carry-over:
- 2 (in 2.480) + 3 (in 3.465) + 1 (in 701.532) + 0 (in 102.100) = 6 and add the 1 carried over = 7
- Write down 7 in the units place.
5. Add the Ones Place:
- Move to the whole numbers, always carrying forward any extra value:
- 0 (in 2.480) + 0 (in 3.465) + 701 (in 701.532) + 102 (in 102.100) = 803
- Write down 803 in the whole number part.
Putting it all together, the result is:
[tex]\[
2.48 + 3.465 + 701.532 + 102.1 = 809.577
\][/tex]
So, the sum of [tex]\(2.48\)[/tex], [tex]\(3.465\)[/tex], [tex]\(701.532\)[/tex], and [tex]\(102.1\)[/tex] is [tex]\(\boxed{809.577}\)[/tex].
