Question

another method of going from one unit to another involves multiplying by a conversion factor. a conversion factor is a fraction that is equal to the number 1. for example, 60 seconds = 1 hour. therefore, 60 sec/1 hr or 1 hr/60 sec = 1. when you multiply by the number 1, the value of the number is not changed, although the units may be different. example: how many milligrams in 20 kilograms? solution: use the following relationships 1000 mg = 1 g 1000 g = 1 kg 1. start with the original number and unit. 2. multiply by a unit - factor with the unit to be discarded on the bottom and the desired unit on top. 3. cancel units. 4. perform numerical calculations 20 kg×1000 g/1 kg×1000 mg/1 g = 20,000,000 or 2×10^7 mg. perform the following conversions using unit - factoring. 1. 500 ml = __ l 2. 25 cg = g 3. 400 mg = kg 4. 30 cm = mm 5. 3500 secs = hr 6. 2 yrs = secs (assume 1 year = 365 days) 7. 15 m = mm 8. 0.75 l = ml 9. 64 kg = g 10. 7200 m = km 11. 4.2 l = cm^3 12. 0.35 km = m 13. 2.3 l = ml 14. 4.5 yds = in 15. 50 mm = km 16. 150 mg = g 17. 150 kg = g 18. 23 ml = l 19. 0.156 g = mg 20. 1.25 l = __ ml

Explanation:

Step1: Recall unit - conversion factors

1 L = 1000 mL, 1 g=100 cg, 1 kg = 1000000 mg, 1 cm = 10 mm, 1 hr = 3600 s, 1 year = 365 days, 1 day = 24 hr, 1 hr= 3600 s, 1 m = 1000 mm, 1 km = 1000 m, 1 in = 36 yds, 1 km = 1000000 mm, 1 g = 1000 mg.

Step2: Perform conversions one - by - one

1. For 500 mL to L: $500\ mL\times\frac{1\ L}{1000\ mL}=0.5\ L$
2. For 25 cg to g: $25\ cg\times\frac{1\ g}{100\ cg}=0.25\ g$
3. For 400 mg to kg: $400\ mg\times\frac{1\ g}{1000\ mg}\times\frac{1\ kg}{1000\ g}=4\times10^{-4}\ kg$
4. For 30 cm to mm: $30\ cm\times\frac{10\ mm}{1\ cm}=300\ mm$
5. For 3500 s to hr: $3500\ s\times\frac{1\ hr}{3600\ s}=\frac{35}{36}\ hr\approx0.972\ hr$
6. For 2 yrs to s: $2\ yrs\times365\ days/yr\times24\ hr/day\times3600\ s/hr = 63072000\ s$
7. For 15 m to mm: $15\ m\times1000\ mm/m = 15000\ mm$
8. For 0.75 L to mL: $0.75\ L\times1000\ mL/L = 750\ mL$
9. For 64 kg to g: $64\ kg\times1000\ g/kg = 64000\ g$
10. For 7200 m to km: $7200\ m\times\frac{1\ km}{1000\ m}=7.2\ km$
11. For 4.2 L to $cm^{3}$: Since 1 L = 1000 $cm^{3}$, $4.2\ L\times1000\ cm^{3}/L = 4200\ cm^{3}$
12. For 0.35 km to m: $0.35\ km\times1000\ m/km = 350\ m$
13. For 2.3 L to mL: $2.3\ L\times1000\ mL/L = 2300\ mL$
14. For 4.5 yds to in: $4.5\ yds\times36\ in/yd = 162\ in$
15. For 50 mm to km: $50\ mm\times\frac{1\ m}{1000\ mm}\times\frac{1\ km}{1000\ m}=5\times10^{-5}\ km$
16. For 150 mg to g: $150\ mg\times\frac{1\ g}{1000\ mg}=0.15\ g$
17. For 150 kg to g: $150\ kg\times1000\ g/kg = 150000\ g$
18. For 23 mL to L: $23\ mL\times\frac{1\ L}{1000\ mL}=0.023\ L$
19. For 0.156 g to mg: $0.156\ g\times1000\ mg/g = 156\ mg$
20. For 1.25 L to mL: $1.25\ L\times1000\ mL/L = 1250\ mL$

Answer:

1. 0.5 L
2. 0.25 g
3. $4\times10^{-4}$ kg
4. 300 mm
5. $\frac{35}{36}$ hr
6. 63072000 s
7. 15000 mm
8. 750 mL
9. 64000 g
10. 7.2 km
11. 4200 $cm^{3}$
12. 350 m
13. 2300 mL
14. 162 in
15. $5\times10^{-5}$ km
16. 0.15 g
17. 150000 g
18. 0.023 L
19. 156 mg
20. 1250 mL