Question

1. 74 cm * 10^(-2)=0.74 meters
2. 8.32 x 10^(-2) kg * 10^(3)=83.2 grams
3. 55.5 ml * 1 cm^(3)/1 ml = 55.5 cm^(3)
4. 0.00527 cal * 10^(-3)=0.00000527 kilocalories
5. 9.52 x 10^(-4) m * 10^(6)=952 micrometers
6. 41.0 ml * 10^(-3)=0.0410 liters
7. 6.0 x 10^(-1) g * 10^(3)=600 mg
8. 8.34 x 10^(-9) cg * 10^(-2)=8.34 x 10^(-11) g
9. 5.0 x 10^(3) mm * 10^(-3)=5.0 m
10. 1 day 24 h/1d 60 m/1h * 60 s/1m = 86400 seconds
11. 5 x 10^(4) mm 10^(-3)10^(-3)=5 x 10^(-2) km
12. 9.1 x 10^(-13) kg = 9.1 x 10^(-1) ng
13. 1 year 12 m/365 d = 8760 hours (approximately)
14. 4.22 cl = 42.2 ml

Explanation:

Step1: Recall metric - conversion factors

1. For length: 1 m = 100 cm, 1 km = 1000 m, 1 m=1000 mm, 1 m = 10^6 micrometers, 1 cm = 10 mm.
2. For mass: 1 kg = 1000 g, 1 g = 1000 mg, 1 g = 100 cg, 1 kg = 10^9 ng.
3. For volume: 1 L = 1000 mL, 1 mL = 1 cm³, 1 L = 100 cL.
4. For energy: 1 kcal = 1000 cal.
5. For time: 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds, 1 year = 365 days (approx.), 1 year = 12 months.

Step2: Perform the conversions

1. $74\ cm\times\frac{1\ m}{100\ cm}=0.74\ m$.
2. $8.32\times 10^{-2}\ kg\times\frac{1000\ g}{1\ kg}=83.2\ g = 8.32\times 10^{1}\ g$.
3. $55.5\ mL\times\frac{1\ cm^{3}}{1\ mL}=55.5\ cm^{3}$.
4. $0.00527\ cal\times\frac{1\ kcal}{1000\ cal}=5.27\times 10^{-6}\ kcal$.
5. $9.52\times 10^{-4}\ m\times\frac{10^{6}\ \mu m}{1\ m}=952\ \mu m=9.52\times 10^{2}\ \mu m$.
6. $41.0\ mL\times\frac{1\ L}{1000\ mL}=0.0410\ L$.
7. $6.0\times 10^{-1}\ g\times\frac{1000\ mg}{1\ g}=600\ mg = 6.0\times 10^{2}\ mg$.
8. $8.34\times 10^{-9}\ cg\times\frac{1\ g}{100\ cg}=8.34\times 10^{-11}\ g$.
9. $5.0\times 10^{3}\ mm\times\frac{1\ m}{1000\ mm}=5.0\ m$.
10. $1\ day\times\frac{24\ h}{1\ day}\times\frac{60\ min}{1\ h}\times\frac{60\ s}{1\ min}=86400\ s$.
11. $5\times 10^{4}\ mm\times\frac{1\ m}{1000\ mm}\times\frac{1\ km}{1000\ m}=5\times 10^{-2}\ km$.
12. $9.1\times 10^{-13}\ kg\times\frac{1000\ g}{1\ kg}\times\frac{10^{9}\ ng}{1\ g}=9.1\times 10^{-1}\ ng$.
13. $1\ year\times\frac{365\ d}{1\ year}\times\frac{24\ h}{1\ d}=8760\ h$.
14. $4.22\ cL\times\frac{1\ L}{100\ cL}\times\frac{1000\ mL}{1\ L}=42.2\ mL$.

Answer:

1. $0.74$
2. $8.32\times 10^{1}$
3. $55.5$
4. $5.27\times 10^{-6}$
5. $9.52\times 10^{2}$
6. $0.0410$
7. $6.0\times 10^{2}$
8. $8.34\times 10^{-11}$
9. $5.0$
10. $86400$
11. $5\times 10^{-2}$
12. $9.1\times 10^{-1}$
13. $8760$
14. $42.2$