Question

5 powers of 10 and scientific notation
convert the following:

1. 510 nm to cm
2. 22 kj to μj
3. 10 μs to days
4. 8 kpc to km (one parsec (pc) is about 3.26 light - years (ly), and one ly is 9 460 730 472 580 800 m)

Explanation:

Step1: Recall conversion factors

1 nm = 10^{-7} cm.

Step2: Convert 1.510 nm to cm

1.510 nm = 1.510×10^{-7} cm.

Step3: Recall conversion factors for energy

1 kJ = 10^{3} J and 1 μJ=10^{- 6} J, so 1 kJ = 10^{9} μJ.

Step4: Convert 2.22 kJ to μJ

2.22 kJ = 2.22×10^{9} μJ.

Step5: Recall conversion factors for time

1 day = 24×60×60 s = 86400 s, 1 μs = 10^{-6} s.

Step6: Convert 10 μs to days

10 μs=10×10^{-6} s = 10^{-5} s. Then, \(\frac{10^{-5}}{86400}\) days=\(\frac{10^{-5}}{8.64\times10^{4}}\) days = 1.16×10^{-10} days.

Step7: Recall conversion factors for length

1 kpc = 10^{3} pc, 1 pc≈3.086×10^{13} km.

Step8: Convert 4.8 kpc to km

4.8 kpc = 4.8×10^{3} pc. Then 4.8×10^{3}×3.086×10^{13} km = 1.48128×10^{17} km.

Answer:

1. 1.510 nm = 1.510×10^{-7} cm
2. 2.22 kJ = 2.22×10^{9} μJ
3. 10 μs = 1.16×10^{-10} days
4. 4.8 kpc = 1.48128×10^{17} km