Question

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.)
2. 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.)
3. how many inches are in one light - year? (3 pts.)

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)

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

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)

$0.188 \times 100\% \approx 19\%$

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