Dimensional Analysis Practice – III KEY Page 1 of 3 1m
1km
×
= 1.50 × 10 –5 km 1000mm 1000m
24h 60min 60sec 1 × 10 9 ns
×
×
×
= 1.296 × 1014 ns 2. 1.50 days ×
1day
1h
min
sec
4qt 32 fl oz
×
= 640 fl oz ⎯sig.
⎯⎯
3. 5gal ×
figs→ 600 fl oz 1gal
1qt
60.0 mi 5280 ft
1h
1min
4. ×
×
×
= 88.0 ft sec h
1mi
60min 60sec
62.0 mi
1km
km
×
= 99.7747 km h ⎯sig.
⎯⎯
5. h figs→ 99.8
h
0.6214 mi
1000m 1000mm
1km ×
×
= 1 × 10 6 mm
km
m
6. 1. 15.0mm ×
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2
1km 2 = (1 × 10 6 mm) = 1 × 1012 mm 2
1 ft = 12in
7. 1 ft 2 = 12in × 12in = 144 in 2
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2
2
43560 ft
144 in
×
= 6272640in 2 ⎯sig.
⎯figs.
⎯→ 6 × 10 6 in 2
2
acre
ft
1m = 1000 mm
1acre ×
8. 1m 2 = 1000 mm × 1000 mm = 1 × 10 6 mm 2
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2
2
6
2
43560 ft
1m
1 × 10 mm
×
= 2.26 × 10 9 mm 2
2 ×
2
acre
10.60 ft
1m
12 mi 1.609 km 1000 m
1h
1min
×
×
×
×
= 5.363 m s2 9. h⋅ sec
1mi
1km
60min 60sec
10. 3.00 × 10 8 m
1km
1mi
60 s 60min
×
×
×
×
= 6.712 × 10 8 mi h ⎯sig.
⎯figs.
⎯→ 6.71 × 10 8 mi h
s
1000 m 1.609 km 1min
h
2000 lbs 16oz
×
= 57600oz 11. 1.80 tons ×
1ton
1lb
1cc = 1cm 3
12. 13.6 g
1lb
946.3cm 3 4 qt
lb
lb
×
×
×
=
113.489
⎯
⎯
⎯
→
113
gal
gal
sig. figs.
cm 3
453.6 g
1qt
gal
3.00 × 10 8 m
1mi
60 s 60min 24hr 365.25 days
×
×
×
×
×
= 5.88 × 1012 mi 13. s
1609 m 1min
1hr
day
y
Part II 20min
1h
×
= 254 h (15240min) 1. 762 mi ×
1mi
60min
0.550 acre ×
Dimensional Analysis Practice – III KEY Page 2 of 3 volume = 2cm × 10.cm × 4 cm = 80cm 3
2. 11.4 g
g
g
80cm 3 ×
=
912
3 ⎯ ⎯⎯→ 900
3
cm
cm
sig. figs.
cm 3
1 ft = 12in
1 ft 3 = 12in × 12in × 12in = 1728in 3
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3. volume = 10.0 ft × 13.0 ft × 8.00 ft = 1040 ft 3
1728in 3
1cm 3
×
= 2.94513 × 10 7 cm 3
1 ft 3
0.06102in 3
1L
4
2.94513 × 10 7 cm 3 ×
3 = 2.945 × 10 L
1000cm
2000 lb 16oz
4. 45 ton ×
×
= 1.4 × 10 6 oz ton
lb
1mi = 5280 ft
volume = 1040 ft 3 ×
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3
5. 1mi 3 = (5280 ft ) = 1.472 × 1011 ft 3
1m 3
1000 L
12
= 4.181 × 1012 L ⎯sig.
⎯⎯
3 ×
figs→ 4 × 10 L
35.21 ft
m3
1.00 g
1lb
946.3cm 3 4 qt
lb
×
×
×
= 8.345 lb gal ⎯sig.
⎯⎯
6. figs→ 8.35 gal cm 3
453.6 g
qt
gal
50 mi 1.609 km
km
×
= 80.45 km h ⎯sig.
⎯⎯
7. figs→ 80. h h
1mi
10.76 ft 2
2
8. 525 m 2 ×
= 5649 ft 2 ⎯sig.
⎯⎯
figs→ 5650 ft
m2
2
1yd = 3 ft; 1yd 2 = ( 3 ft ) = 9 ft 2
1.472 × 1011 ft 3 ×
9. area of ceiling = 24.0 ft × 51.0 ft = 1224 ft 2 €
1yd 2
= 136 yd 2
9 ft 2
2000 lb 1gal
×
= 1029.16 gal ⎯sig.
⎯⎯
10. 3tons ×
figs→ 1000 gal ton
5.83lb
11. 1728in 3
1gal
3
volume of bathtub = 4 ft × 6 ft × 3 ft = 72 ft ×
×
= 538.597 gal ⎯sig.
⎯⎯
3
figs→ 540 gal
ft
231 ft 3
8.3lb
= 4470 lb ⎯sig.
⎯⎯
12. 538.597 gal ×
figs→ 4500 lb gal
4 qt
1L
13.6 kg
×
×
= 27719.66 kg ⎯sig.
⎯⎯
13. 538.597 gal ×
figs→ 28000 kg gal 1.057qt
L
60 s 186000 mi
14. 17.6min×
×
= 1.96416 × 10 8 mi ⎯sig.
⎯⎯
→ 1.96 × 10 8 mi figs
min
s
33.81 fl oz
15. 22.7 L ×
= 767.487 fl oz ⎯sig.
⎯⎯
→ 767 fl oz figs
L
1224 ft 2 ×
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Dimensional Analysis Practice – III KEY 1000 g 1mL
×
= 113.64 mL ⎯sig.
⎯⎯
figs→ 114 mL kg
22.0 g
1L
1.84 kg
×
= 0.920 kg 17. 500 mL ×
1000 mL
L
⎛
12in ⎞
5 ft +11in = ⎜ 5 ft ×
⎟ +11in = 60in +11in = 71in
ft ⎠
⎝
18. 1m
71in ×
= 1.8034 m ⎯sig.
⎯⎯
→ 1.8 m
figs
39.37in
16. 2.50 kg ×
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