Math Homework CH. 1 and 2

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Chapter 1

Notes about rounding off. 

Significant digits. If a problem has 2 significant digits in each number, the answer can only have two significant digits. If it has 3 significant digits to two decimal places, the answer has significant digits to two decimal places. The purpose of these has to do with accuracy of measurements. Follow the rules in Chapter one.

Rounding to the nearest whole number follows rules learned in elementary school math.  Ex: rounding to 1 or 2, if the answer is from 1.0 to 1.4, the answer is 1; from 1.5 to 2.0, the answer is 2. Using calculators, if an answer is 1.4999999, it will be rounded down to 1. In practical use in a lab, the sensitivity of an instrument may limit the accuracy of a measurement to one decimal place. Then all digits to the right of the first decimal place are ignored as inaccurate.

Perform the following calculations and round off significant digits in your answers. 

How are the following numbers expressed in scientific notation? (Ch. 1.2.1)

  1. 0.00044 = 
  2. 10,820 x 103 =  How are the following numbers expressed in decimal notation? (Ch. 1.2.2)
  3. 2.6 x 10-7 = 
  4. 6.47 x 105 = 
  5. (1.9 x 10-2) – (9.8 x 10-3) = 
  6.  (4.15 x 106) x (2.85 x 10-4)  = 
  • If a virus has 12,400 basepairs, how many kilobase pairs is this? (Ch. 1.3)
  • Convert 0.835 mL into microliters. (Ch. 1.3.1)  
  • Convert 1.89 picomoles into micromoles and express your answer in scientific notation.
    To convert moles to micromoles, we use the following conversion factor:
  1. A solution holds a concentration of DNA molecules = 300 ng/L. If the student pipets 5 L into a tube, how many total micrograms are in the tube? 

Chapter 2

  1. You are preparing 350 mL of a 5X buffer using a 20X stock solution. (Ch. 2.1, 2.2)
    1. How much 20X stock do you use (in mL)? 
  • How much water do you use to dilute the stock (in mL)? 
  • You are preparing 600 mL of a 0.9% w/v solution of NaCl.  How many grams of solid NaCl do you use? (Ch. 2.3)
  • You are preparing 285 mL of 70% (v/v) ethanol in water using a 95% ethanol stock. Round your answer to the nearest whole number. (Ch. 2.4)
    • How much 95% ethanol (in mL) do you use? 
  • How much water (in mL) do you add? 
  • You are preparing 250 mL of gel mix for protein electrophoresis, which requires a final concentration of 1.6% SDS. The lab has a 10% stock solution of SDS. How much SDS stock solution (in mL) do you use? Round your answer to the nearest whole number. (Ch. 2.1)
  • You are preparing 300 mL of a 17 mM Tris solution by dissolving solid Tris in water (MW Tris = 121.14 g/mol.). How many mg of Tris do you use? Round your answer to the nearest whole number. (Ch. 2.5.1)
  • You are preparing 1,400 mL of a 0.08 M EDTA solution by dissolving solid EDTA in water (MW EDTA = 292.24 g/mol). How many grams of EDTA do you use (round your answer to the nearest whole number)? (Ch. 2.1, 2.5.1)
  • You need to prepare 15 mL of a 2 mM CaCl2 solution for an experiment, and the lab has a stock solution at 1.5 M.  (Ch. 2.1, 2.5.1, 2.5.3)
    • How much stock solution (in microliters) do you use? 
  • How much water (in mL) do you use? Answer to two decimal places. 
  • The hydrogen ion concentration in a solution of strong acid is 2.0 x 10-2 M. What is the solution’s pH? Answer to one decimal place. (Ch. 2.7).