Question

multiple-step dimensional analysis practice (introductory chemistry podcasts 4 and 5)
multiple-step dimensional analysis problems are solved in the same manner as one-step dimensional analysis problems. so, if you could do the one-step, you can do any dimensional analysis problem! all you have to do is set up the problem so that your units continuously cancel out until you are left with the unit you want at the end. please view introductory chemistry podcast 4 and 5: on dimensional analysis for a refresher on how to solve these problems. many of the problems can be solved more than one way. at minimum, choose five problems from page 1, five problems from page 2 and two problems from page 3 (total = 12 problems minimum). i strongly encourage you to attempt all problems.
directions: solve the following dimensional analysis problems. show all work.

1. how many inches are there in a football field (100 yards)? 1 yard = 3 feet; 1 foot = 12 inches
2. how many walking paces are there approximately as you walk down main street (0.25 miles)? 1 mile = 5280 feet; 1 foot = 12 inches; 22 inches = 1 walking pace
3. how many feet are between the first and second story of a building (1 story)? 1 story = 3.33 meters; 100 centimeters = 1 meter; 1 inch = 2.54 cm; 1 foot = 12 inches
4. how many hours are in a fortnight (2 weeks)? 1 week = 7 days; 1 day = 24 hours
5. how many decades are equal to 1.7 × 10²⁵ minutes? 60 min = 1 hour; 24 hours = 1 day; 7 days = 1 week; 52 weeks = 1 year; 10 years = 1 decade

Explanation:

Problem 1:

Step1: Convert yards to feet

We know 1 yard = 3 feet, so for 100 yards, the number of feet is $100\ \text{yards} \times \frac{3\ \text{feet}}{1\ \text{yard}}$.
$100\times3 = 300\ \text{feet}$

Step2: Convert feet to inches

We know 1 foot = 12 inches, so for 300 feet, the number of inches is $300\ \text{feet} \times \frac{12\ \text{inches}}{1\ \text{foot}}$.
$300\times12 = 3600\ \text{inches}$

Step1: Convert miles to feet

We know 1 mile = 5280 feet, so for 0.25 miles, the number of feet is $0.25\ \text{miles} \times \frac{5280\ \text{feet}}{1\ \text{mile}}$.
$0.25\times5280 = 1320\ \text{feet}$

Step2: Convert feet to inches

We know 1 foot = 12 inches, so for 1320 feet, the number of inches is $1320\ \text{feet} \times \frac{12\ \text{inches}}{1\ \text{foot}}$.
$1320\times12 = 15840\ \text{inches}$

Step3: Convert inches to walking paces

We know 22 inches = 1 walking pace, so the number of walking paces is $15840\ \text{inches} \times \frac{1\ \text{walking pace}}{22\ \text{inches}}$.
$\frac{15840}{22}= 720\ \text{walking paces}$

Step1: Convert meters to centimeters

We know 1 meter = 100 centimeters, so for 3.33 meters, the number of centimeters is $3.33\ \text{meters} \times \frac{100\ \text{centimeters}}{1\ \text{meter}}$.
$3.33\times100 = 333\ \text{centimeters}$

Step2: Convert centimeters to inches

We know 1 inch = 2.54 cm, so the number of inches is $333\ \text{centimeters} \times \frac{1\ \text{inch}}{2.54\ \text{centimeters}}$.
$\frac{333}{2.54}\approx131.1\ \text{inches}$

Step3: Convert inches to feet

We know 1 foot = 12 inches, so the number of feet is $131.1\ \text{inches} \times \frac{1\ \text{foot}}{12\ \text{inches}}$.
$\frac{131.1}{12}\approx10.93\ \text{feet}$ (or approximately 11 feet)

Answer:

3600 inches

Problem 2: