1) Round 578.683 m, 47.3333 kg, and 789.5 cm to four significant figures.

2) Find the weight of a 12.25 kg dog. Round your answer to the correct number of significant figures. Use weight=massxfree-fall acceleration.
3) Round 3155.24m, 8.777 73 cm, and 93.775 57 kg to one less significant figure than they each have currrently.
4) Multiply 4.135 x 4.688 888 887 m x 8.7m round your answer to the correct number of significant figures.

PLEASE explain each of the answers to me in simple language. I need to submit these by tonight and I struggled and I know my answers are wrong. Thank you.

4) Multiply 4.135 x 4.688 888 887 m x 8.7m round your answer to the correct number of significant figures.

============================
You only have 2 sig figs because you said
8.7 not 8.70000000
so
19.388555555
is
19 <-------answer

1) Round 578.683 m, 47.3333 kg, and 789.5 cm to four significant figures.

0,1,2,3,4 round down
5,6,7,8,9 round up

578.6 83
8 is greater than 4
so this becomes
578.7 meters

47.33 33
3 is less than 4 so this becomes
47.33 kilograms

789.5 cm
This already has four significant figures

3) Round 3155.24m, 8.777 73 cm, and 93.775 57 kg to one less significant figure than they each have currently.

====================
3155.24
4 is less than 5 so
3155.3

3<5 so
8.7777

93.77557
7>5 so
93.7756

2) Find the weight of a 12.25 kg dog. Round your answer to the correct number of significant figures. Use weight=massxfree-fall acceleration.

g is different in different places on earth. We need it to four significant figures because your mass is to four sig figs.
I will call 9.806 65 m/s^2 = 9.807 m/s^2

m g = weight = 12.25 * 9.807 = 120.1 Newtons

1) To round numbers to four significant figures, we start counting from the leftmost nonzero digit and stop at the fourth digit. For the given numbers:

- 578.683 m: This number already has four significant figures, so it doesn't need rounding.
- 47.3333 kg: The leftmost nonzero digit is 4, and we count four digits from there, so the rounded number is 47.33 kg.
- 789.5 cm: The leftmost nonzero digit is 7, and we count four digits from there, so the rounded number is 789.5 cm.

2) The weight of an object is given by the formula weight = mass x free-fall acceleration. We can use the value of the free-fall acceleration on Earth, which is approximately 9.8 m/s^2.

Given that the mass of the dog is 12.25 kg:
weight = 12.25 kg x 9.8 m/s^2
weight = 120.05 N (approximately)

Since the mass is given to four significant figures, we round the weight to four significant figures as well:
weight = 120.1 N.

3) To round numbers to one less significant figure, we start counting from the leftmost nonzero digit and stop at the second digit. For the given numbers:

- 3155.24 m: The leftmost nonzero digit is 3, and we count one digit from there, so the rounded number is 3000 m.
- 8.777 73 cm: The leftmost nonzero digit is 8, and we count one digit from there, so the rounded number is 8.8 cm.
- 93.775 57 kg: The leftmost nonzero digit is 9, and we count one digit from there, so the rounded number is 90 kg.

4) To multiply numbers while considering significant figures, we count the significant figures in each number and round the result to the least number of significant figures.

- 4.135 x 4.688 888 887 m: The number 4.135 has four significant figures, and the number 4.688 888 887 has ten significant figures. Since the second number has the fewest significant figures (four), we round the multiplication result to four significant figures. The product is approximately 19.34 m.

- 19.34 m x 8.7 m: Both numbers have four significant figures, so we can multiply them directly. The product is 168.258 m^2.

Rounding the result to four significant figures, we get approximately 168.3 m^2.

1) To round a number to four significant figures, start from the leftmost non-zero digit and count four digits. Check the digit to the right of the fourth digit:

- If it is less than 5, simply remove all digits to the right of the fourth digit.
- If it is 5 or greater, round up the fourth digit and remove all digits to the right.

For example:

- Round 578.683 m: The leftmost non-zero digit is 5. The fourth digit is 6, which is greater than 5. Thus, we round up the fourth digit to 7 and remove all digits to the right. The rounded value is 578.7 m.

- Round 47.3333 kg: The leftmost non-zero digit is 4. The fourth digit is 3, which is less than 5. Therefore, we remove all digits to the right, and the rounded value is 47.33 kg.

- Round 789.5 cm: The leftmost non-zero digit is 7. The fourth digit is 5, which is exactly 5. In this case, we round up the fourth digit to 6 and remove all digits to the right. The rounded value is 790 cm.

2) To find the weight of the dog, we use the formula weight = mass x free-fall acceleration. The mass of the dog is given as 12.25 kg. The free-fall acceleration on Earth is approximately 9.8 m/s².

Weight = 12.25 kg x 9.8 m/s² = 120.05 N.

Since the number 9.8 has three significant figures, we round our answer to match the least number of significant figures, which is two (from 12.25 kg). Therefore, the rounded weight of the dog is 120 N.

3) To round a number to one less significant figure, start from the leftmost non-zero digit and count one digit. If the digit to the right of it is 5 or greater, round up the selected digit and remove all digits to the right. If the digit to the right is less than 5, simply remove all digits to the right.

For example:

- Round 3155.24 m: The leftmost non-zero digit is 3. We count one digit, which is 1. The digit to the right of 1 is 5, so we round up the selected digit to 2 and remove all digits to the right. The rounded value is 3200 m.

- Round 8.77773 cm: The leftmost non-zero digit is 8. We count one digit, which is 7. The digit to the right of 7 is 3, so we remove all digits to the right. The rounded value is 7 cm.

- Round 93.77557 kg: The leftmost non-zero digit is 9. We count one digit, which is 3. The digit to the right of 3 is 7, so we round up the selected digit to 4 and remove all digits to the right. The rounded value is 90 kg.

4) To multiply numbers and round to the correct number of significant figures, multiply the numbers as usual and then round the result to match the least number of significant figures among the numbers being multiplied.

For example:

- Multiply 4.135 m by 4.688888887 m: The product of these numbers is 19.369037440695 m². Since the least number of significant figures among the numbers being multiplied is three (from 4.688888887 m), we round the product to three significant figures. The rounded value is 19.4 m².

Thank you Damon