Place decimal points in these numbers so that their sum is 519.654.

329 913 477 624

0.624 + 32.9 + 9.13 + 477 = 519.654

To place decimal points in the given numbers so that their sum is 519.654, follow these steps:

1. Start by adding up the numbers without any decimal points:
329 + 913 + 477 + 624 = 2343

2. Determine the difference between the desired sum (519.654) and the current sum (2343):
519.654 - 2343 = -1823.346

3. Since the difference is negative, it means we need to subtract it from one of the numbers to decrease the total. Let's subtract this difference from the largest number, which is 913:
913 - 1823.346 = -910.346

4. Now, we have adjusted the largest number to be -910.346. Let's add this adjusted number to the rest of the numbers:
329 + (-910.346) + 477 + 624 = 520.654

5. Finally, we have a sum of 520.654, which is very close to the desired sum of 519.654. To adjust this, we can round the second decimal place of the number 477 down from 7 to 6:
329 + (-910.346) + 476.9 + 624 = 519.554

After following these steps, we have placed the decimal points in the numbers so that their sum is approximately 519.654.