### Solution:
Let's walk through the process of rounding the given numbers to 3, 4, and 5 significant figures.
#### a) 612737
1. Rounding to 3 significant figures:
- Start with the first three significant digits: 612.
- Look at the digit right after the third significant figure, which is 7.
- Since 7 is greater than or equal to 5, we round up the third digit:
- 612 becomes 613.
- Replace all digits after the rounded digit with zeros: 613000.
Result: 612737 rounded to 3 significant figures is 612700.
2. Rounding to 4 significant figures:
- Start with the first four significant digits: 6127.
- Look at the digit right after the fourth significant figure, which is 3.
- Since 3 is less than 5, we do not round up:
- 6127 remains 6127.
- Replace all digits after the rounded digit with zeros: 613000.
Result: 612737 rounded to 4 significant figures is 613000.
3. Rounding to 5 significant figures:
- Start with the first five significant digits: 61273.
- Look at the digit right after the fifth significant figure, which is 7.
- Since 7 is greater than or equal to 5, we round up the fifth digit:
- 61273 becomes 61274.
- Replace all digits after the rounded digit with zeros: 610000.
Result: 612737 rounded to 5 significant figures is 610000.
#### b) 18.2990
1. Rounding to 3 significant figures:
- Start with the first three significant digits: 18.2.
- Look at the digit right after the third significant figure, which is 9.
- Since 9 is greater than or equal to 5, we round up the third digit:
- 18.29 becomes 18.3.
Result: 18.2990 rounded to 3 significant figures is 18.3.
2. Rounding to 4 significant figures:
- Start with the first four significant digits: 18.29.
- Look at the digit right after the fourth significant figure, which is 9.
- Since 9 is greater than or equal to 5, we round up the fourth digit:
- 18.299 remains 18.299.
Result: 18.2990 rounded to 4 significant figures is 18.299.
3. Rounding to 5 significant figures:
- Start with the first five significant digits: 18.299.
- Look at the digit right after the fifth significant figure, which is 0.
- Since 0 is less than 5, we do not round up:
- 18.2990 remains 18.299.
Result: 18.2990 rounded to 5 significant figures is 18.299.
### Final Results:
- 612737 rounded to:
- 3 significant figures: 612700,
- 4 significant figures: 613000,
- 5 significant figures: 610000.
- 18.2990 rounded to:
- 3 significant figures: 18.3,
- 4 significant figures: 18.299,
- 5 significant figures: 18.299.
