Answer :
Sure! Let's solve each of these problems step by step, and make sure we maintain the correct number of significant figures.
### a) [tex]\(98.1 \times 0.03\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(98.1\)[/tex] has 3 significant figures.
- [tex]\(0.03\)[/tex] has 1 significant figure.
2. Perform the multiplication:
- Calculate [tex]\(98.1 \times 0.03 = 2.943\)[/tex].
3. Round the result to the least number of significant figures in the given numbers, which is 1:
- The first significant figure of [tex]\(2.943\)[/tex] is 2, so the answer is rounded to 2.9 (keeping 1 significant figure).
### b) [tex]\(57 \times 7.368\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(57\)[/tex] has 2 significant figures.
- [tex]\(7.368\)[/tex] has 4 significant figures.
2. Perform the multiplication:
- Calculate [tex]\(57 \times 7.368 = 420.976\)[/tex].
3. Round the result to the least number of significant figures in the given numbers, which is 2:
- The first two significant figures of [tex]\(420.976\)[/tex] are 42, so the result is rounded to 420.98 (keeping 2 significant figures).
### c) [tex]\(\frac{8.578}{4.33821}\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(8.578\)[/tex] has 4 significant figures.
- [tex]\(4.33821\)[/tex] has 6 significant figures.
2. Perform the division:
- Calculate [tex]\(8.578 \div 4.33821 = 1.977344057\)[/tex].
3. Round the result to the least number of significant figures in the given numbers, which is 4:
- The first four significant figures of [tex]\(1.977344057\)[/tex] are 1.977, so the answer is 1.9773 (keeping 4 significant figures).
To summarize the results with the correct number of significant figures:
- [tex]\(98.1 \times 0.03 = 2.9\)[/tex]
- [tex]\(57 \times 7.368 = 420.98\)[/tex]
- [tex]\(\frac{8.578}{4.33821} = 1.9773\)[/tex]
If you have any more questions or need further clarification, feel free to ask!
### a) [tex]\(98.1 \times 0.03\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(98.1\)[/tex] has 3 significant figures.
- [tex]\(0.03\)[/tex] has 1 significant figure.
2. Perform the multiplication:
- Calculate [tex]\(98.1 \times 0.03 = 2.943\)[/tex].
3. Round the result to the least number of significant figures in the given numbers, which is 1:
- The first significant figure of [tex]\(2.943\)[/tex] is 2, so the answer is rounded to 2.9 (keeping 1 significant figure).
### b) [tex]\(57 \times 7.368\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(57\)[/tex] has 2 significant figures.
- [tex]\(7.368\)[/tex] has 4 significant figures.
2. Perform the multiplication:
- Calculate [tex]\(57 \times 7.368 = 420.976\)[/tex].
3. Round the result to the least number of significant figures in the given numbers, which is 2:
- The first two significant figures of [tex]\(420.976\)[/tex] are 42, so the result is rounded to 420.98 (keeping 2 significant figures).
### c) [tex]\(\frac{8.578}{4.33821}\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(8.578\)[/tex] has 4 significant figures.
- [tex]\(4.33821\)[/tex] has 6 significant figures.
2. Perform the division:
- Calculate [tex]\(8.578 \div 4.33821 = 1.977344057\)[/tex].
3. Round the result to the least number of significant figures in the given numbers, which is 4:
- The first four significant figures of [tex]\(1.977344057\)[/tex] are 1.977, so the answer is 1.9773 (keeping 4 significant figures).
To summarize the results with the correct number of significant figures:
- [tex]\(98.1 \times 0.03 = 2.9\)[/tex]
- [tex]\(57 \times 7.368 = 420.98\)[/tex]
- [tex]\(\frac{8.578}{4.33821} = 1.9773\)[/tex]
If you have any more questions or need further clarification, feel free to ask!
