Question

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. 6.4 kg = ____ g
10. 7200 m = ____ km

Explanation:

Step1: Recall conversion factors

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

Step2: Convert 400 mg to kg

$400\ mg\times\frac{1\ g}{1000\ mg}\times\frac{1\ kg}{1000\ g}=\frac{400}{1000\times1000}\ kg = 0.0004\ kg$

Step3: Convert 30 cm to mm

$30\ cm\times\frac{10\ mm}{1\ cm}=300\ mm$

Step4: Convert 3500 s to hr

$3500\ s\times\frac{1\ hr}{3600\ s}=\frac{3500}{3600}\ hr=\frac{35}{36}\ hr\approx0.972\ hr$

Step5: Convert 2 yrs to s

$2\ yrs\times\frac{365\ days}{1\ yr}\times\frac{24\ hrs}{1\ day}\times\frac{3600\ s}{1\ hr}=2\times365\times24\times3600\ s = 63072000\ s$

Step6: Convert 15 m to mm

$15\ m\times\frac{1000\ mm}{1\ m}=15000\ mm$

Step7: Convert 0.75 L to mL

$0.75\ L\times\frac{1000\ mL}{1\ L}=750\ mL$

Step8: Convert 6.4 kg to g

$6.4\ kg\times\frac{1000\ g}{1\ kg}=6400\ g$

Step9: Convert 7200 m to km

$7200\ m\times\frac{1\ km}{1000\ m}=7.2\ km$

Answer:

1. $0.0004$ kg
2. $300$ mm
3. $\frac{35}{36}\ hr\approx0.972$ hr
4. $63072000$ s
5. $15000$ mm
6. $750$ mL
7. $6400$ g
8. $7.2$ km