Honors Chemistry Summer Assignment: You should have some experience with this material but in honors chemistry, we may be using it in more advanced ways than what you are used to. The purpose of this assignment is to help you familiarize yourself with these math skills so that you may more readily use them to understand and solve chemistry related problems. This assignment will focus on Scientific Notation, the Metric System, and Dimensional Analysis. If the provided explanations are not complete enough to help you complete the assignment, consider watching some online tutorials such as those provided by Khan Academy (https://www.khanacademy.org/). The following several pages include a brief introduction to the three topics addressed on this assignment as well as some sample problems. You are encouraged to solve these sample problems and confirm that you are completing them correctly by looking at the answer key provided on Page 5. Page 6 includes some problems you will need to solve. Page 6 is due on Thursday August 10 th as your first homework assignment. We will be taking a no calculator quiz on Friday August 11th over these topics! For the record, you will need a SCIENTIFIC CALCULATOR for this course and will be permitted to use it on most occasions, however we will not be using calculators for the first week or for this assignment as working outside of a calculator will help you strengthen your skills. You will be amazed how much easier problem solving can be when you work with your brain instead of a calculator One final thing before we begin. This assignment is not meant to scare you away from the course or stress you out before the year has even begun! If you find that you are completely lost with this material AFTER GENUINELY TRYING TO COMPLETE IT, your instructor will be able to help you with this if you are still struggling in class when you meet. 1
Section 1: Scientific Notation You will need to familiarize yourself with scientific notation and how to perform calculations using it. Sometimes it is not feasible to simply put things in standard notation but working with scientific notation on a calculator can be frustrating. Scientific Notation is simply a way to write a number using x 10 n to convey how big or small the number is. Scientific notation always starts with a single non-zero figure. For example, the number 2500 can be expressed as 2.5 x 10 3. 10 3 means 10x10x10 or 1000 Numbers smaller than 1 can also be expressed in scientific notation. When you raise something to a negative power, it is the same as dividing by that value raised to the positive value. Example: One more thing, anything raised to the 0 power equals 1. So if you want to express a number between 1 and 10 in scientific notation, you simply use 10 1. For example: Write the following numbers in scientific notation: 1. 24000 2. 230 3. 123456789 4. 0.000432 5. 0.0112 6. 0.123 Write the following numbers in standard notation: 7. 3.5 x 10 4 8. 1.02 x 10 7 9. 3.5 x 10-6 10. 2.0 x 10-1 11. 5.0 x 10 0 2
Calculations Involving Scientific Notation: You will not always be able to punch numbers into your calculator, and scientific notation can be difficult to use with a calculator properly. Luckily, scientific notation exists because there is an easy trick with exponents when all of them have the same base value: Let s say you want to multiply a bunch of numbers that are all in scientific notation. Since all of them will have 10 being raised to some power, you can simply add the exponents of the tens together to get the final exponent. Example: You can also do something like this when dividing. You just subtract instead: Say you wish to multiply to figures written in scientific notation together: One approach is to put both numbers into standard notation and then multiply them together. Then put the answer in scientific notation. Another approach is to ignore the scientific notation and multiply the values together, then simplify the powers of 10, then combine the two. 2250 Try to complete the following calculations WITHOUT A CALCULATOR, ANSWERS MUST BE WRITTEN IN SCIENTIFIC NOTATION. 12. (4.00 x 10 4 ) (2.00 x 10-2 ) 13. (9.0 x 10 6 ) (3.0 x 10-2 ) 14. (2.0 x 10 2 ) (1.0 x 10-4 ) 15. (1.50 x 10 7 ) (2 x 10 65 ) 16. (3.00 x 10 7 ) (4.00 x 10-3 ) / (2.00 x 10 2 ) 17. (2.00 x 10 1 ) / (4.00 x 10 0 ) 3
Section 2: The Metric System You should work on memorizing the following metric prefixes and what they abbreviate. Try to understand the quantity that they represent (example, kilo means 1000 or 10 3 ). Most of you learned to do this using King Henry Died by Drinking Chocolate Milk. While this pneumatic device is handy for remembering which prefixes are larger and how many times you should move the decimal, Simply moving the decimal to do your conversions is not always going to work and you are also expected to know the actual values of the prefixes themselves, not just how much bigger or smaller they are. Metric Prefixes Number of Units Represented Example Kilo 10 3 5 km = 5000 m Hecto 10 2 7.5 hg = 750 g Deka 10 1 4.34 dal = 43.4 L Deci 10-1 0.54 dm = 0.054 m Centi 10-2 245.0 cm = 2.450 m Milli 10-3 435 mg = 0.435 g Micro 10-6 3.0 µg = 0.0000030 g Nano 10-9 1000000000 ng = 1 g Pico 10-12 25.4 pm = 0.0000000000254 m Section 3: Dimensional Analysis: We will be doing a great deal of unit converting in this course. We will be using something called Dimensional Analysis to do these conversions. This involves multiply a measurement by a fraction where the wanted unit is in the numerator and the unwanted unit is in the denominator. For example, the following shows the use of dimensional analysis to convert 15.5 grams into milligrams. = 0.0155 mg Notice that the fraction used for the unit conversion has 1 mg in the numerator and 10-3 g in the denominator, this is showing how many grams are in 1 milligram. As long as the figure in the numerator has the same value as the one in the denominator, the conversion will work. The gram unit cancels out and is replaced with the milligram unit. The same conversion can be done by looking at how many milligrams are in 1 gram instead: = 0.0155 mg Perform the following unit conversions using dimensional analysis. WITHOUT A CALCULATOR, ANSWERS MUST BE WRITTEN IN SCIENTIFIC NOTATION. 18. 1.0 x 10 1 kg g 19. 4.50 x 10 9 pm m 20. 2.25 x 10 8 m km 4
21. 4.50 x 10 17 µg kg 22. 5.00 x 10 0 L cl Practice Problems Answer Key 1. 2.4 x 10 4 2. 2.3 x 10 2 3. 1.23456789 x 10 8 4. 4.32 x 10-4 5. 1.12 x 10-2 6. 1.23 x 10-1 7. 35000 8. 10200000 9. 0.0000035 10. 0.2 11. 5 12. 4 x 2 = 8 and 10 4 x 10-2 = 10 4+(-2) = 10 2 Multiplying 8 and 10 2 gives the correct answer which is, 8.0 x 10 2 13. 9 x 3 = 27 and 10 6 x 10-2 = 10 6+(-2) = 10 4 27 x 10 4 is not scientific notation as there can be only one non-zero to the left of the decimal place. Therefore, the correct answer is 2.7 x 10 5 (the decimal is moved one place to the left which means it will need to be multiplied by 10 one more time) Another way to think about that last part is to write 27 in scientific notation, 2.7 x 10 1 and then multiply it by 10 4 giving us 2.7 x 10 1+4 14. 2 x 1 = 2 and 10 2 x 10-4 = 10-2 Answer is 2 x 10-2 15. 1.5 x 2 = 3 and 10 7 x 10 65 = 10 72 Answer is 3 x 10 72 16. 3 x 4 / 2 = 6 and 10 7 x 10-3 / 10 2 = 10 7+(-3)-2 = 10 2 Answer is 6 x 10 2 17. 2 / 4 = 0.5 and 10 1 / 10 0 = 10 1-0 = 10 1 The answer is 0.5 x 10 1, but we must report it as 5 x 10 0 (the decimal is moved one place to the right which means it will need to be multiplied by 10 one less time) 18. = 1 x 10 4 g 19. = 4.5 x 10-3 m 20. = 2.25 x 10 5 km 21. = 4.50 x 10 8 kg 5
22. = 5.00 x 10 2 cl Honors Chemistry Summer Homework Problems: All answers must be written in scientific notation. These problems should be solved without the use of a calculator. Perform the following conversions: A. How many micrograms are in 2.50 x 10 4 grams? B. How many kilometers are in 1.75 x 10 7 milliliters? C. How many centimeters are in 4.01 x 10 3 picometers? Perform the following calculations: A. (4.50 x 10-4 ) / (2.00 x 10-7 ) B. (6.00 x 10 9 )(4.00 x 10 3 ) / (2.00 x 10 3 )(3.00 x 10 2 ) C. (120)(2.00 x 10 5 )/(0.0002) 6
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