Question

a major task in many of the problems is units. there are many different units in the metric units, and some in cgs system. there is a chart of the more useful conversion facts. dimensional analysis, designed to help you with several conversion problems for you to complete. make the conversions indicated and report. convert the following: 1. 2.35 mi to m 2. 8.903 x 10⁴ cm to mm 3. 2.1 gal to ft³ 4. 29876 kg to lb 5. 3 n to lbf 6. 243° to radians 7. 56.3 mi/h to m/s

Explanation:

Step1: Recall mile - meter conversion

1 mile = 1609.34 m.

Step2: Calculate for 2.35 mi

$2.35\times1609.34 = 3781.949$ m

Step3: Recall cm - mm conversion

1 cm = 10 mm.

Step4: Calculate for $8.903\times10^{4}$ cm

$(8.903\times 10^{4})\times10=8.903\times 10^{5}$ mm

Step5: Recall gallon - cubic - foot conversion

1 gal = 0.133681 ft³.

Step6: Calculate for 2.1 gal

$2.1\times0.133681 = 0.28073$ ft³

Step7: Recall kg - lb conversion

1 kg = 2.20462 lb.

Step8: Calculate for 29876 kg

$29876\times2.20462=65855.90712$ lb

Step9: Recall newton - pound - force conversion

1 N = 0.224809 lbf.

Step10: Calculate for 3 N

$3\times0.224809 = 0.674427$ lbf

Step11: Recall degree - radian conversion

1 degree=$\frac{\pi}{180}$ radians.

Step12: Calculate for 243°

$243\times\frac{\pi}{180}=\frac{27\pi}{20}\approx 4.24115$ radians

Step13: Recall mile - km conversion

1 mile = 1.60934 km.

Step14: Calculate for 56.3 mi

$56.3\times1.60934 = 90.606842$ km

Answer:

1. 3781.949 m
2. $8.903\times 10^{5}$ mm
3. 0.28073 ft³
4. 65855.90712 lb
5. 0.674427 lbf
6. $\frac{27\pi}{20}\approx 4.24115$ radians
7. 90.606842 km