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AR Chemistry: Required Math Skills Name_____________________________________ The math skills required for success in chemistry are equal to "hard algebra 1". The following set includes instructions on how to calculate answers. These instructions may not be within your current comfort zone but they have been used over twenty-seven years and have led to success for many students in college chemistry. A. Rounding in Decimal Places Ex: Round the following number to 1 decimal place. 875.64973 Instructions: 875.X4963 875.X4--- 1. Cover the place you are rounding up 2. Look at the next number to the right (ignore all the other numbers to the right!!!!) 3. Round the number a. For 0 - 4, round down keeping the covered number the same. b. For 5 - 9, round the covered number up 875.6 Ex: '5' rounds up, so 'X' goes up one 4973.652 4973.X54973.7 Set A: 1. 2. 3. 4. 5. Round 987.5634 to two decimal places Round 1.9328 to three decimal places Round 264.5823 to one decimal place Round 12.34999 to one decimal place Round 37.666667 to two decimal places _____________________ _____________________ _____________________ _____________________ _____________________ 987.56 1.933 264.6 12.3 37.67 B. Rounding in Non-Decimal Places Instructions: 1. Same as above -- cover the number to be rounded and round up and down as necessary 2. Put "Place Holding Zeros" so your number is still in its range (eg. 1000's to 1000's) Example: 1. 2. 3. Round 578434.5 to the third number from the left Cover the third number and look at the fourth number Round the number, in this case, keeping it the same Add Placeholder zeros to fill the spots on the left of decimal 578434.5 57X4--.578 - - -.578000 Set B: Round each of the following numbers to the third number from the left 1. 2. 3. 4. 5. 1. 87400 6. 872000 87393.34 92762 201003 643832.38982 3838383 2. 92800 7. 215000 _______ _______ _______ _______ _______ 3. 201000 8. 938000 4. 644000 9. 383000 6. 7. 8. 9. 10. 872400.4 215439 937593 382974 676767600 5. 3840000 10. 677 000 000 _______ _______ _______ _______ _______ C. Fraction Bars: ALL FRACTION BARS WILL BE HORIZONTAL!!!!!!!!!!!!! Example: Write out the fraction three-fifths (three divided by five) 3 Answer: -------NOT 3 / 5 5 Set C: Convert each of the following problems into horizontal fraction bars 1. (2/9) _____________________ 2 9 2. (3/5) x (7/8) _____________________ 3 x 7 5 8 3. (4/7) x (1/3) _____________________ 4 x 1 7 3 4. (6/7) x (2/9) _____________________ 6 x 2 7 9 D. Multiplication of stringed fractions DO NOT Multiply ALL THE TOPS, write it down, then the bottoms, etc. Instructions: Example: For numbers on top, hit 'X' then put the number in For numbers on the bottom, hit ' / ' then put the number in When all numbers have been entered, hit EQUAL 3.4 15.6 7.9 37.5 x -------- x --------- x -------- = 59.9805xxxx 6.7 4.6 8.5 2 ways: Alternate top and bottom --> All tops then all bottoms --> 37.5 x 3.4 / 6.7 x 15.6 / 4.6 x 7.9 / 8.5 = 37.5 x 3.4 x 15.6 x 7.9 / 6.7 / 4.6 / 8.5 = Set D: Calculate the following problems. Don't worry about the number of numbers in your answer 1. 1.2 67.5 x -------9.7 12.6 4.9 x --------- x -------- = 2.6 8.7 _______________________ 22.7922..... 2. 9.6 18.5 x -------1.7 25.6 4.9 x --------- x -------- = 8.6 3.5 _______________________ 435.375..... 3. 3.4 31.1 x -------6.7 15.6 7.9 x --------- x -------- = 4.6 8.5 _______________________ 49.7438.... E. Cross Multiplication and Division (Cross multiply and divide) Instructions: Ex: Solve (5.6)(9.4) = (8.34)(x) (1.7) (5.8) 1. Multiply the top left and the bottom right and put on one side of equal sign (5.6)(9.4)(5.8) = 2. Multiply the bottom left and top right and put on the other side of equal sign (5.6)(9.4)(5.8) = (1.7)(8.34)(x) 3. Divide both sides by the numbers multiplied on the unknown's side (5.6)(9.4)(5.8) = (1.7)(8.34) (x) (1.7)(8.34) (1.7)(8.34) 4. Multiply and divide using the top-multiply and bottom-divide method in section D 5.6 x 9.4 / 1.7 x 5.8 / 8.34 = x x = 215. 3407xxxxxx ****We will learn a method, later, that allows you to solve the problem with JUST your calculator!!! Set E: Calculate the following problems to solve for the unknown (the Letter) 1. (3.57)(2.78) = (6.7)(V) 9.45 44.5 = ___________________ 6.975.... 2. (P)(27.8) = (6.7)(44.1) 298 273 = ___________________ 11.601.... 3. (3.57)(9.78) = (1.5)(8.65) T 273 = ___________________ 734.61.... 4. (1.57)(9.78) = (P)(21.6) 298 303 = ___________________ 0.7227...... 5. (3.57)(86.9) = (6.7)(38.2) 545 T = ___________________ 449.62...... F. Scientific Notation 1. Scientific notation puts a number into a form that is: ex: 2. 10x 9.11 x 10-31 6.02 x 1023 a number between 1 and 10 multiplied by 10 to a power 6.67 x 10-11 4.42 x 106 IF 'x' is a positive number, the number is greater than one. IF 'x' is a negative number, the number is less than one. ex: 2.3 x 104 = 23000 2.3 x 10-4 = 0.00023 3. How to put into your calculator the number 2.3 x 10-4 a. Scientific Calculator: Find 'EE' or 'EXP' button 1. Type in: 2.3 EE -4 = You will get either 0.00023 or 2.3 -4 (means 2.3 x 10-4) or 2.3 E-4 b. Graphing Calculator : Find 'EE' or 'EXP button -- usually have to hit 2nd to activate it 1. Type in: 2.3 2nd EE -4 Enter 2. Do NOT use the math system of: 2.3 x 10 (to the) -4 4. Multiplication -- just like before -- putting the numbers in is the hard part Ex: Solve 3.01 x 10 Scientific Calculator: Graphing Calculator: 23 x 44.01 ------------------ = 146.7 9.03 x 1022 3.01 Exp 23 x 44.01 / 9.03 Exp 22 = 3.01 2nd EE 23 x 44.01 / 9.03 2nd EE 22 = Set F: Calculate the following problems using the methods above 39.34 6.02 x 1023 x -------------- = 18.02 1.2 x 10 23 3. 39.34 4.56 x 106 x -------------- = 67.8 2. 40.18 5.7 x 1024 x -------------- = 6.02 x 1023 1. 2. 180.18 x -------------- = 6.02 x 1023 _________________ 1.314 E24 or 1.314 24 _________________ 35.91 _________________ 2.645 E6 or 2.645 06 or 2645876 _________________ 380.44