Question

a major task in many of the problems in th units. there are many different units in thi metric units, and some in cgs system met chart of the more useful conversion facts. dimensional analysis, designed to help y several conversion problems for you to cor make the conversions indicated and report
convert the following:

1. 2.35 mi to m
2. 8.903 x 10^(-6) cm to nm
3. 2.1 gal to ft^3
4. 2.90876 kg to lbs
5. 3 n to lbs
6. 243° to radians
7. 56.3 mi/h to m/s
8. 94.5 ft/s to mi/hr

Explanation:

Step1: Recall mile - meter conversion

1 mile = 1609.34 m. So, for 2.35 mi, we multiply by the conversion factor.
$2.35\times1609.34 = 3782.949$ m

Step2: Recall centimeter - nanometer conversion

1 cm = 10,000,000 nm. For $8.903\times 10^{-6}$ cm, we multiply by the conversion factor.
$(8.903\times 10^{-6})\times10^{7}=89.03$ nm

Step3: Recall gallon - cubic - foot conversion

1 gal = 0.133681 ft³. For 2.1 gal, we multiply by the conversion factor.
$2.1\times0.133681 = 0.28073$ ft³

Step4: Recall kilogram - pound conversion

1 kg = 2.20462 lbs. For 2.90876 kg, we multiply by the conversion factor.
$2.90876\times2.20462\approx6.413$ lbs

Step5: Recall newton - pound conversion

1 N = 0.224809 lbs. For 3 N, we multiply by the conversion factor.
$3\times0.224809 = 0.674427$ lbs

Step6: Recall degree - radian conversion

To convert degrees to radians, we use the formula $radians=\frac{\pi}{180}\times degrees$. For 243°, we have:
$\frac{\pi}{180}\times243=\frac{27\pi}{20}\approx 4.24$ radians

Step7: Recall mile - hour to meter - second conversion

1 mi = 1609.34 m and 1 h = 3600 s. For 56.3 mi/h:
$56.3\times\frac{1609.34}{3600}\approx25.17$ m/s

Step8: Recall foot - second to mile - hour conversion

1 mi = 5280 ft and 1 h = 3600 s. For 94.5 ft/s:
$94.5\times\frac{3600}{5280}\approx64.4$ mi/h

Answer:

1. 3782.949 m
2. 89.03 nm
3. 0.28073 ft³
4. 6.413 lbs
5. 0.674427 lbs
6. $\frac{27\pi}{20}\approx 4.24$ radians
7. 25.17 m/s
8. 64.4 mi/h