Question

1. 46 cm to m
2. 499 dl to cl
3. 105 cm to kilometers
4. 0.0031 mm to km
5. 5.46×10⁻⁵ g to μg
6. 465 000 ng to mg
7. 8500 cm to km
8. 6.7×10⁶ μl to ml
9. 48 000 000 kg to mg
10. 780 mm to m
11. 5m/s to km/h
12. 100 km/h to m/s

Explanation:

Step1: Recall conversion factors

1 m = 100 cm, 1 dL = 10 cL, 1 km = 100000 cm, 1 km = 1000000000 mm, 1 g = 1000000 μg, 1 mg = 1000000 ng, 1 km = 100000 cm, 1 mL = 1000 μL, 1 kg = 1000000 mg, 1 m = 1000 mm, 1 km = 1000 m, 1 h=3600 s.

Step2: Convert 46 cm to m

Since 1 m = 100 cm, then $46\ cm=\frac{46}{100}m = 0.46m$.

Step3: Convert 499 dL to cL

Since 1 dL = 10 cL, then $499\ dL=499\times10 cL = 4990cL$.

Step4: Convert 105 cm to km

Since 1 km = 100000 cm, then $105\ cm=\frac{105}{100000}km=0.00105km$.

Step5: Convert 0.0031 mm to km

Since 1 km = 1000000000 mm, then $0.0031\ mm=\frac{0.0031}{1000000000}km = 3.1\times10^{-12}km$.

Step6: Convert $5.46\times 10^{-5}$ g to μg

Since 1 g = 1000000 μg, then $5.46\times 10^{-5}\ g=5.46\times 10^{-5}\times1000000 μg = 54.6μg$.

Step7: Convert 465000 ng to mg

Since 1 mg = 1000000 ng, then $465000\ ng=\frac{465000}{1000000}mg = 0.465mg$.

Step8: Convert 8500 cm to km

Since 1 km = 100000 cm, then $8500\ cm=\frac{8500}{100000}km = 0.085km$.

Step9: Convert $6.7\times 10^{6}$ μL to mL

Since 1 mL = 1000 μL, then $6.7\times 10^{6}\ μL=\frac{6.7\times 10^{6}}{1000}mL=6700mL$.

Step10: Convert 48000000 kg to mg

Since 1 kg = 1000000 mg, then $48000000\ kg=48000000\times1000000 mg=4.8\times 10^{13}mg$.

Step11: Convert 780 mm to m

Since 1 m = 1000 mm, then $780\ mm=\frac{780}{1000}m = 0.78m$.

Step12: Convert 5 m/s to km/h

$5\ m/s=5\times\frac{3600}{1000}km/h=18km/h$.

Step13: Convert 100 km/h to m/s

$100\ km/h = 100\times\frac{1000}{3600}m/s=\frac{100000}{3600}m/s=\frac{250}{9}m/s\approx27.78m/s$.

Answer:

1. 0.46 m
2. 4990 cL
3. 0.00105 km
4. $3.1\times 10^{-12}$ km
5. 54.6 μg
6. 0.465 mg
7. 0.085 km
8. 6700 mL
9. $4.8\times 10^{13}$ mg
10. 0.78 m
11. 18 km/h
12. $\frac{250}{9}m/s\approx27.78m/s$