1. einstein the dog weighs 74 pounds. how much does he weigh in grams? solve using dimensional analysis…

1. einstein the dog weighs 74 pounds. how much does he weigh in grams? solve using dimensional analysis. dont forget about significant figures! note: 2.2 pounds = 1 kilogram (4 pts.)\n2. a student is calculating the density of calcium in lab. he calculates the density to be 1.25 g/cm³. when he looks up the actual density of calcium in a chemistry handbook, he finds that the accepted value is 1.54 g/cm³. calculate his percent error. round your percent to the correct number of significant figures. (3 pts.)\n3. how many inches are in one light - year? (3 pts.)

1. einstein the dog weighs 74 pounds. how much does he weigh in grams? solve using dimensional analysis. dont forget about significant figures! note: 2.2 pounds = 1 kilogram (4 pts.)\n2. a student is calculating the density of calcium in lab. he calculates the density to be 1.25 g/cm³. when he looks up the actual density of calcium in a chemistry handbook, he finds that the accepted value is 1.54 g/cm³. calculate his percent error. round your percent to the correct number of significant figures. (3 pts.)\n3. how many inches are in one light - year? (3 pts.)

Answer

Explanation:

Step1: Convert pounds to kilograms

$74\ \text{lbs} \times \frac{1\ \text{kg}}{2.2\ \text{lbs}} \approx 33.636\ \text{kg}$

Step2: Convert kilograms to grams

$33.636\ \text{kg} \times 1000\ \text{g/kg} = 33636\ \text{g}$

Step3: Apply significant figures (2 sig figs)

$33636\ \text{g} \approx 34000\ \text{g}$

Explanation:

Step1: Calculate absolute difference

$|1.25 - 1.54| = 0.29$

Step2: Divide by accepted value

$\frac{0.29}{1.54} \approx 0.188$

Step3: Multiply by 100% and round (2 sig figs)

$0.188 \times 100% \approx 19%$

Explanation:

Step1: Calculate seconds in a year

$365\ \text{days} \times 24\ \text{h/day} \times 60\ \text{min/h} \times 60\ \text{s/min} = 31536000\ \text{s}$

Step2: Distance in meters (c=3e8 m/s)

$3 \times 10^8\ \text{m/s} \times 31536000\ \text{s} = 9.4608 \times 10^{15}\ \text{m}$

Step3: Convert meters to inches (1m=39.37in)

$9.4608 \times 10^{15}\ \text{m} \times 39.37\ \text{in/m} \approx 3.73 \times 10^{17}\ \text{in}$

Answer:

34000 grams 19% $3.73 \times 10^{17}$ inches