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Answer :
Sure! Let's solve each equation step by step, focusing on how we determine the correct number of significant figures for each result.
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:
- [tex]\(98.1 \times 0.03 = 2.943\)[/tex]
3. Round the result to the least number of significant figures from the numbers being multiplied, which is 1.
- Rounded result: [tex]\(2.9\)[/tex]
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:
- [tex]\(57 \times 7.368 = 419.976\)[/tex]
3. Round the result to 2 significant figures.
- Rounded result: [tex]\(420\)[/tex] (considered [tex]\(4.2 \times 10^2\)[/tex] for significant figures)
c. [tex]\(8.578 / 4.33821\)[/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:
- [tex]\(8.578 / 4.33821 = 1.9773132236567614\)[/tex]
3. Round the result to 4 significant figures.
- Rounded result: [tex]\(1.977\)[/tex]
d. [tex]\(6.90 / 2.8952\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(6.90\)[/tex] has 3 significant figures.
- [tex]\(2.8952\)[/tex] has 5 significant figures.
2. Perform the division:
- [tex]\(6.90 / 2.8952 = 2.383255042829511\)[/tex]
3. Round the result to 3 significant figures.
- Rounded result: [tex]\(2.38\)[/tex]
These steps ensure that each result is presented with the correct number of significant figures according to the rules of significant digits in multiplication and division.
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:
- [tex]\(98.1 \times 0.03 = 2.943\)[/tex]
3. Round the result to the least number of significant figures from the numbers being multiplied, which is 1.
- Rounded result: [tex]\(2.9\)[/tex]
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:
- [tex]\(57 \times 7.368 = 419.976\)[/tex]
3. Round the result to 2 significant figures.
- Rounded result: [tex]\(420\)[/tex] (considered [tex]\(4.2 \times 10^2\)[/tex] for significant figures)
c. [tex]\(8.578 / 4.33821\)[/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:
- [tex]\(8.578 / 4.33821 = 1.9773132236567614\)[/tex]
3. Round the result to 4 significant figures.
- Rounded result: [tex]\(1.977\)[/tex]
d. [tex]\(6.90 / 2.8952\)[/tex]
1. Identify the number of significant figures in each number:
- [tex]\(6.90\)[/tex] has 3 significant figures.
- [tex]\(2.8952\)[/tex] has 5 significant figures.
2. Perform the division:
- [tex]\(6.90 / 2.8952 = 2.383255042829511\)[/tex]
3. Round the result to 3 significant figures.
- Rounded result: [tex]\(2.38\)[/tex]
These steps ensure that each result is presented with the correct number of significant figures according to the rules of significant digits in multiplication and division.
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