Sure, let's solve each equation while considering significant figures:
### 1. Division: [tex]\( \frac{3.256}{2.7} \)[/tex]
First, let's determine the significant figures:
- The number [tex]\( 3.256 \)[/tex] has 4 significant figures.
- The number [tex]\( 2.7 \)[/tex] has 2 significant figures.
In division, the result should be reported with the same number of significant figures as the number with the fewest significant figures.
- Therefore, the result should have 2 significant figures.
Perform the division:
[tex]\[ \frac{3.256}{2.7} \approx 1.206 \][/tex]
However, since the result should have 2 significant figures:
[tex]\[ 1.206 \approx 1.2 \][/tex]
Therefore, the final result for [tex]\( \frac{3.256}{2.7} \)[/tex] is 1.2.
### 2. Multiplication: [tex]\( 14.88 \times 3.77 \)[/tex]
Determine the significant figures:
- The number [tex]\( 14.88 \)[/tex] has 4 significant figures.
- The number [tex]\( 3.77 \)[/tex] has 3 significant figures.
In multiplication, the result should be reported with the same number of significant figures as the number with the fewest significant figures.
- Therefore, the result should have 3 significant figures.
Perform the multiplication:
[tex]\[ 14.88 \times 3.77 \approx 56.0976 \][/tex]
Since the result should have 3 significant figures:
[tex]\[ 56.0976 \approx 56.1 \][/tex]
Therefore, the final result for [tex]\( 14.88 \times 3.77 \)[/tex] is 56.1.
### 3. Multiplication: [tex]\( 12.699 \times 5 \)[/tex]
Determine the significant figures:
- The number [tex]\( 12.699 \)[/tex] has 5 significant figures.
- The number [tex]\( 5 \)[/tex] has 1 significant figure.
In multiplication, the result should be reported with the same number of significant figures as the number with the fewest significant figures.
- Therefore, the result should have 1 significant figure.
Perform the multiplication:
[tex]\[ 12.699 \times 5 \approx 63.495 \][/tex]
Since the result should have 1 significant figure:
[tex]\[ 63.495 \approx 60 \][/tex]
Therefore, the final result for [tex]\( 12.699 \times 5 \)[/tex] is 60.
