Answer :
Let's solve the measurements step-by-step with the correct number of significant digits:
1. Division: [tex]\( \frac{355.99 \, \text{g}}{59.1 \, \text{mL}} \)[/tex]
- First, perform the division: [tex]\( 355.99 \div 59.1 \)[/tex].
- In division, the result should have the same number of significant figures as the number with the least significant figures in the calculation. Here, 355.99 has 5 significant figures, while 59.1 has 3 significant figures.
- The result is therefore rounded to 3 significant figures: [tex]\( 6.02 \, \frac{\text{g}}{\text{mL}} \)[/tex].
2. Multiplication: [tex]\( 78.1 \, \frac{\text{g}}{\text{mL}} \times 37 \, \text{mL} \)[/tex]
- First, perform the multiplication: [tex]\( 78.1 \times 37 \)[/tex].
- The result should be rounded to the number of significant figures of the least precise measurement. Here, 78.1 has 3 significant figures, and 37 has 2 significant figures.
- The result is therefore rounded to 2 significant figures: [tex]\( 2900 \, \text{g} \)[/tex].
3. Multiplication: [tex]\( 7.81 \, \frac{\text{g}}{\text{mL}} \times 3.525 \, \text{mL} \)[/tex]
- First, perform the multiplication: [tex]\( 7.81 \times 3.525 \)[/tex].
- The result should be rounded to the least number of significant figures, which is 3 in both measurements (7.81 and 3.525 have 3 significant figures each).
- The result is therefore rounded to 3 significant figures: [tex]\( 27.5 \, \text{g} \)[/tex].
By following these steps and applying the rules for significant figures, we arrive at the final results:
- [tex]\( 6.02 \, \frac{\text{g}}{\text{mL}} \)[/tex]
- [tex]\( 2900 \, \text{g} \)[/tex]
- [tex]\( 27.5 \, \text{g} \)[/tex]
1. Division: [tex]\( \frac{355.99 \, \text{g}}{59.1 \, \text{mL}} \)[/tex]
- First, perform the division: [tex]\( 355.99 \div 59.1 \)[/tex].
- In division, the result should have the same number of significant figures as the number with the least significant figures in the calculation. Here, 355.99 has 5 significant figures, while 59.1 has 3 significant figures.
- The result is therefore rounded to 3 significant figures: [tex]\( 6.02 \, \frac{\text{g}}{\text{mL}} \)[/tex].
2. Multiplication: [tex]\( 78.1 \, \frac{\text{g}}{\text{mL}} \times 37 \, \text{mL} \)[/tex]
- First, perform the multiplication: [tex]\( 78.1 \times 37 \)[/tex].
- The result should be rounded to the number of significant figures of the least precise measurement. Here, 78.1 has 3 significant figures, and 37 has 2 significant figures.
- The result is therefore rounded to 2 significant figures: [tex]\( 2900 \, \text{g} \)[/tex].
3. Multiplication: [tex]\( 7.81 \, \frac{\text{g}}{\text{mL}} \times 3.525 \, \text{mL} \)[/tex]
- First, perform the multiplication: [tex]\( 7.81 \times 3.525 \)[/tex].
- The result should be rounded to the least number of significant figures, which is 3 in both measurements (7.81 and 3.525 have 3 significant figures each).
- The result is therefore rounded to 3 significant figures: [tex]\( 27.5 \, \text{g} \)[/tex].
By following these steps and applying the rules for significant figures, we arrive at the final results:
- [tex]\( 6.02 \, \frac{\text{g}}{\text{mL}} \)[/tex]
- [tex]\( 2900 \, \text{g} \)[/tex]
- [tex]\( 27.5 \, \text{g} \)[/tex]
