multiple - step dimensional analysis practice (introductory chemistry podcasts 4 and 5)\nso, if you could do…

multiple - step dimensional analysis practice (introductory chemistry podcasts 4 and 5)\nso, 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 a 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.\ndirections: solve the following dimensional analysis problems. show all work.\n1. how many inches are there in a football field (100 yards)? 1 yard = 3 feet; 1 foot = 12 inches\n100yd×3ft1yd×12in1ft = 3,600in\n2. 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\n0.25m1mile×5280ft1mile×12in1ft×1wp22in = 720 walking pace\n3. 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\n1story3.33m×1m100cm×2.54in1cm×12in1ft = 0.0915 or 0.092 ft\n4. how many hours are in a fortnight (2 weeks)? 1 week = 7 days; 1 day = 24 hours\n2weeks1week×7days1week×24hrs1day = 336 hours\n5. 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\n6. on average, there are 3 pages in every chapter of a james patterson novel. each book has approximately 79 chapters. james patterson has published 58 books. approximately how many pages has james patterson written?\n7. houston has approximately 2,210,000 million people. each person has 2 hands and each hand has 5 fingers. how many fingers are in houston? answer in scientific notation.\n2,210,000mp1p×1p2h×1h5f = 221,000f

multiple - step dimensional analysis practice (introductory chemistry podcasts 4 and 5)\nso, 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 a 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.\ndirections: solve the following dimensional analysis problems. show all work.\n1. how many inches are there in a football field (100 yards)? 1 yard = 3 feet; 1 foot = 12 inches\n100yd×3ft1yd×12in1ft = 3,600in\n2. 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\n0.25m1mile×5280ft1mile×12in1ft×1wp22in = 720 walking pace\n3. 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\n1story3.33m×1m100cm×2.54in1cm×12in1ft = 0.0915 or 0.092 ft\n4. how many hours are in a fortnight (2 weeks)? 1 week = 7 days; 1 day = 24 hours\n2weeks1week×7days1week×24hrs1day = 336 hours\n5. 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\n6. on average, there are 3 pages in every chapter of a james patterson novel. each book has approximately 79 chapters. james patterson has published 58 books. approximately how many pages has james patterson written?\n7. houston has approximately 2,210,000 million people. each person has 2 hands and each hand has 5 fingers. how many fingers are in houston? answer in scientific notation.\n2,210,000mp1p×1p2h×1h5f = 221,000f

Answer

Explanation:

Step1: Solve problem 5

First, convert minutes to decades using the given conversion - factors. [ \begin{align*} 1.7\times 10^{25}\text{ min}&=\frac{1.7\times 10^{25}\text{ min}}{1}\times\frac{1\text{ hr}}{60\text{ min}}\times\frac{1\text{ day}}{24\text{ hr}}\times\frac{1\text{ week}}{7\text{ day}}\times\frac{1\text{ year}}{52\text{ week}}\times\frac{1\text{ decade}}{10\text{ year}}\ &=\frac{1.7\times 10^{25}}{60\times24\times7\times52\times10}\text{ decades}\ &=\frac{1.7\times 10^{25}}{60\times24\times7\times52\times10}\ &=\frac{1.7\times 10^{25}}{5241600}\ &=\frac{1.7\times 10^{25}}{5.2416\times 10^{6}}\ &=(1.7\div5.2416)\times10^{25 - 6}\ &\approx0.324\times 10^{19}\ &=3.24\times 10^{18}\text{ decades} \end{align*} ]

Step2: Solve problem 6

Multiply the number of pages per chapter, number of chapters per book, and number of books. [3\text{ pages/chapter}\times79\text{ chapters/book}\times58\text{ books}=3\times79\times58\text{ pages}=3\times4582\text{ pages}=13746\text{ pages}]

Step3: Solve problem 7

Correct the dimensional - analysis setup for the number of fingers in Houston. [2210000\text{ people}\times\frac{2\text{ hands}}{1\text{ person}}\times\frac{5\text{ fingers}}{1\text{ hand}} = 2210000\times2\times5\text{ fingers}=22100000\text{ fingers}=2.21\times 10^{7}\text{ fingers}]

Answer:

Problem 5: $3.24\times 10^{18}$ decades Problem 6: 13746 pages Problem 7: $2.21\times 10^{7}$ fingers