Answer :
Sure, let's go through the solution step by step!
### Part 1: Solve the Equations
#### a. [tex]\( 98.1 \times 0.03 \)[/tex]
- Significant Figures: 98.1 has 3 significant figures, and 0.03 has 1 significant figure. The result should be rounded to the least number, which is 1 significant figure.
- Calculation: [tex]\( 98.1 \times 0.03 = 2.943 \)[/tex]
- Rounded Result: 2.9 (rounded to 1 significant figure)
#### b. [tex]\( \frac{57}{368} \)[/tex]
- Significant Figures: 57 has 2 significant figures, and 368 has 3 significant figures. The result should be rounded to the least number, which is 2 significant figures.
- Calculation: [tex]\( \frac{57}{368} = 0.15489 \)[/tex]
- Rounded Result: 0.15 (rounded to 2 significant figures)
#### c. [tex]\( \frac{8.578}{4.33821} \)[/tex]
- Significant Figures: 8.578 has 4 significant figures, and 4.33821 has 6 significant figures. The result should be rounded to 4 significant figures.
- Calculation: [tex]\( \frac{8.578}{4.33821} = 1.977346 \)[/tex]
- Rounded Result: 1.9773 (rounded to 4 significant figures)
### Part 2: Count Significant Figures in Each Term
#### a. [tex]\(140 \times 10^3\)[/tex]
- Significant Figures: 140 has 2 significant figures assuming no specified decimal point, and [tex]\(10^3\)[/tex] doesn't count towards significant figures.
- Total Significant Figures: 2
#### b. 6.01
- Significant Figures: 3
#### c. 02947.1
- Significant Figures: Leading zeros are not significant. Total = 5
#### d. 583.02
- Significant Figures: 5
### Part 3: Round off to 3 Significant Figures
#### a. 140000
- Rounded to 3 significant figures: 140000 (remains the same)
#### b. 6.01
- Rounded to 3 significant figures: 6.01
#### c. 0.29471
- Rounded to 3 significant figures: 0.295
#### d. 583.02
- Rounded to 3 significant figures: 583
I hope this step-by-step solution helps you understand how to handle each part regarding significant figures and rounding! If you have any further questions or need more explanation on any point, feel free to ask!
### Part 1: Solve the Equations
#### a. [tex]\( 98.1 \times 0.03 \)[/tex]
- Significant Figures: 98.1 has 3 significant figures, and 0.03 has 1 significant figure. The result should be rounded to the least number, which is 1 significant figure.
- Calculation: [tex]\( 98.1 \times 0.03 = 2.943 \)[/tex]
- Rounded Result: 2.9 (rounded to 1 significant figure)
#### b. [tex]\( \frac{57}{368} \)[/tex]
- Significant Figures: 57 has 2 significant figures, and 368 has 3 significant figures. The result should be rounded to the least number, which is 2 significant figures.
- Calculation: [tex]\( \frac{57}{368} = 0.15489 \)[/tex]
- Rounded Result: 0.15 (rounded to 2 significant figures)
#### c. [tex]\( \frac{8.578}{4.33821} \)[/tex]
- Significant Figures: 8.578 has 4 significant figures, and 4.33821 has 6 significant figures. The result should be rounded to 4 significant figures.
- Calculation: [tex]\( \frac{8.578}{4.33821} = 1.977346 \)[/tex]
- Rounded Result: 1.9773 (rounded to 4 significant figures)
### Part 2: Count Significant Figures in Each Term
#### a. [tex]\(140 \times 10^3\)[/tex]
- Significant Figures: 140 has 2 significant figures assuming no specified decimal point, and [tex]\(10^3\)[/tex] doesn't count towards significant figures.
- Total Significant Figures: 2
#### b. 6.01
- Significant Figures: 3
#### c. 02947.1
- Significant Figures: Leading zeros are not significant. Total = 5
#### d. 583.02
- Significant Figures: 5
### Part 3: Round off to 3 Significant Figures
#### a. 140000
- Rounded to 3 significant figures: 140000 (remains the same)
#### b. 6.01
- Rounded to 3 significant figures: 6.01
#### c. 0.29471
- Rounded to 3 significant figures: 0.295
#### d. 583.02
- Rounded to 3 significant figures: 583
I hope this step-by-step solution helps you understand how to handle each part regarding significant figures and rounding! If you have any further questions or need more explanation on any point, feel free to ask!
