Question

name
u1 w3 hw#3- solving inequalities & dimensional analysis
block
due date: fr
conversions:
1 foot = 12 inches
3 ft = 1 yard
5280 ft = 1 mile
1 inch = 2.54 cm
1 km = 0.62 miles
dimensional analysis
1000 mm = 1 m
100 cm = 1 m
10 mm = 1 cm
1 km = 1000 m
60 sec = 1 min
60 min = 1 hr
24 hr = 1 day
365 days = 1 yr
using the above conversion factors, make the following conversions

1. convert 100 mm into inches.
2. convert 32 years into hours.
3. convert 12,345 mm into km.
4. convert 12,345 seconds into years.
5. convert 35 inches into meters.
6. convert 1234 mm into feet.
7. convert 27 km/hr into m/s.
8. convert 35 miles/hr into ft/sec.

Explanation:

1. Convert 100 mm into inches.

Step1: Convert mm to cm

We know that \(10\space mm = 1\space cm\), so to convert 100 mm to cm, we divide by 10.
\(100\space mm\times\frac{1\space cm}{10\space mm}= 10\space cm\)

Step2: Convert cm to inches

We know that \(1\space inch = 2.54\space cm\), so to convert cm to inches, we divide by 2.54.
\(10\space cm\times\frac{1\space inch}{2.54\space cm}\approx3.94\space inches\)

Step1: Convert years to days

We know that \(365\space days = 1\space year\), so for 32 years, we multiply by 365.
\(32\space years\times\frac{365\space days}{1\space year}= 11680\space days\)

Step2: Convert days to hours

We know that \(24\space hours = 1\space day\), so we multiply the number of days by 24.
\(11680\space days\times\frac{24\space hours}{1\space day}= 280320\space hours\)

Step1: Convert mm to m

We know that \(1000\space mm = 1\space m\), so we divide 12345 mm by 1000.
\(12345\space mm\times\frac{1\space m}{1000\space mm}= 12.345\space m\)

Step2: Convert m to km

We know that \(1000\space m = 1\space km\), so we divide the number of meters by 1000.
\(12.345\space m\times\frac{1\space km}{1000\space m}= 0.012345\space km\)

Answer:

\(\approx 3.94\) inches

2. Convert 32 years into hours.