Question

study guide for dimensional analysis test
directions: convert the units using the cancellation method. round to the hundredths place in all problems.
1 m = 1000 mm 1 kg = 1000 g 1 mi = 5,280 ft 1 hr = 60 min
1 m = 100 cm 1 yr = 365 days 1 cm³ = 1 ml 1 l = 1000 ml
1 ft = 12 in 1 day = 24 hr 1 km = 1000 m

1. convert 6.81 miles to inches.
2. convert 990 cm³ to l.
3. convert 6.98 kg to g.
4. convert 563.3 min to hr.
5. convert 24 yr to hr.
6. convert 647,012 cm to km.
7. 8.05 m to mm.
8. 90,087 ml to l.
9. convert 47 eggs to dozens.
10. convert 218.6 cm to m.

Explanation:

Step1: Convert 6.81 miles to inches

We know that 1 mi = 5280 ft and 1 ft = 12 in. So, $6.81\ mi\times\frac{5280\ ft}{1\ mi}\times\frac{12\ in}{1\ ft}=6.81\times5280\times12\ in = 432748.80\ in$.

Step2: Convert 990 $cm^{3}$ to L

Since 1 $cm^{3}$ = 1 mL and 1 L = 1000 mL, then $990\ cm^{3}\times\frac{1\ mL}{1\ cm^{3}}\times\frac{1\ L}{1000\ mL}=0.99\ L$.

Step3: Convert 6.98 kg to g

Given 1 kg = 1000 g, so $6.98\ kg\times\frac{1000\ g}{1\ kg}=6980.00\ g$.

Step4: Convert 563.3 min to hr

As 1 hr = 60 min, then $563.3\ min\times\frac{1\ hr}{60\ min}\approx9.39\ hr$.

Step5: Convert 24 yr to hr

We know 1 yr = 365 days and 1 day = 24 hr. So, $24\ yr\times\frac{365\ days}{1\ yr}\times\frac{24\ hr}{1\ day}=24\times365\times24\ hr = 210240.00\ hr$.

Step6: Convert 647012 cm to km

Since 1 m = 100 cm and 1 km = 1000 m, then $647012\ cm\times\frac{1\ m}{100\ cm}\times\frac{1\ km}{1000\ m}=6.47012\ km\approx6.47\ km$.

Step7: Convert 8.05 m to mm

Given 1 m = 1000 mm, so $8.05\ m\times\frac{1000\ mm}{1\ m}=8050.00\ mm$.

Step8: Convert 90087 mL to L

Since 1 L = 1000 mL, then $90087\ mL\times\frac{1\ L}{1000\ mL}=90.087\ L$.

Step9: Convert 47 eggs to dozens

As 1 dozen = 12 eggs, so $47\ eggs\times\frac{1\ dozen}{12\ eggs}\approx3.92\ dozens$.

Step10: Convert 218.6 cm to m

Given 1 m = 100 cm, then $218.6\ cm\times\frac{1\ m}{100\ cm}=2.186\ m\approx2.19\ m$.

Answer:

1. 432748.80 in
2. 0.99 L
3. 6980.00 g
4. 9.39 hr
5. 210240.00 hr
6. 6.47 km
7. 8050.00 mm
8. 90.09 L
9. 3.92 dozens
10. 2.19 m