1.1 Math skills required in this course

As a freshman chemistry student, it is your responsibility to ensure that you can do the basic types of math discussed in this letter. Your grade depends on being familiar with the math requirements in the course. This math is nothing new—you have been taught this over the years. This instruction should only be a review of what you already know.

1) Algebra:

Algebra is used to solve equations by un-doing whatever is being done to an unknown variable. For example, if an equation has “x+2” then you would subtract “2” to solve for “x”. Everything that is done to one side must be done to the other side of the equation as well.

Visit the following websites and observe how algebraic equations are manipulated.

On the Khan Academy website make sure you solve the practice problems

https://www.khanacademy.org/math/algebra2/modeling-with-algebra#manipulating-formulas

Simplify the following:

1. X+ b= c

X?

Subtract b from both sides

X+b-b= c-b

X= c -b

2. X/A= B

X=?

X= A x B

3. F/X= G

X=?

X= F/G

A/B / R/S=?? Ans: AS/BR

12 / 4/3= Ans is 9 not 1

2) Review on Exponentials

Practice:

Express in nonexponential form.

1. 10³ = 10 x 10 x 10 = 1000 (The exponent tells you how many zeroes)
2. 10⁷ = 10,000,000
3. 10¹ = 10 (Exponent of 1 tells you there is one zero)
4. 10⁰ = 1 (Exponent of zero tells you there is no zero. Also, remember that anything to the power of zero equals to 1.)
5. 10^-3 = ? (There are two ways to look at this.) A negative exponent means it is the inverse, or reciprocal. 10^–3 = 1/103 = 1/1000 = 0.001 (one thousandth) Or, you can consider 10^-3 = 1 x 10^-3. To convert to the nonexponential form, the exponent must increase by 3, from –3 to 0. This means the decimal point must move 3 places to the left of 1. Thus, 10^-3 = 0.001
6. 10^-6 = 0.000001 (Decimal is 6 places to the left of 1).
7.When you raise an exponent to a power, you multiply the exponents. (10^a )^b= 10^{a x b}

1. (10³ ) ⁴ = 10^3×4 = 10¹² = 1,000,000,000,000
2. (10^–1) ³ = 10^–3 = 0.001
3. (2 x 10^–2) ³ = 2³ x 10^–6 = 8 x 10^–6 = 0.000008
4. (2 + 10² ) ² = (2 + 100)² = 102² = 10404 (2 + 10² ) 2 is NOT (2² + 10⁴ ) which would give you the wrong answer of 10004! The distributive property in question 3 above does not apply when you are doing an addition or subtraction within the parenthesis.

3) Calculator tips:
Ask your instructor on how to operate your calculator

4) Order of Operations:
Even though your calculator may know some of the rules below and do it correctly, you need to know the rules yourself so that you enter the numbers in the right order. This is the order:

1. Do operations inside the parenthesis first.
2. Do logarithms, and powers next.
3. Do multiplication and divisions next.
4. Do addition and subtraction last.

Given the problem: 4 + 9 ÷ 3 − 2 x 3 + (3 + 1) x 4 First think about which operation must be done FIRST. First you do 9 ÷ 3 = 3 and 2 x 3 = 6 and (3+1) = 4 and so (3+1) x 4 becomes 4 x 4 = 16. Then you do 4 + 3 − 6 + 16 = 17 So 4 + 9 ÷ 3 − 2 x 3 + (3 + 1) x 4 = 4 + 3 − 6 + 16 = 17 (The correct answer is 17.)

Now try it with your calculator. Try entering in exactly the same order as written: 4 + 9 ÷ 3 – 2 x 3 + (3+1) x 4 You should be getting the same answer of 17. Unless you have an ancient calculator, your calculator should know to do the operations inside a parenthesis, and the multiplication and division first before addition and subtraction. What you don’t want to do is to press ENTER after 4+9 before pressing ÷ 3. If you did, you are telling the calculator to do 4+9 before dividing by 3, but the problem does not tell you to add first. You are supposed to do 9 ÷3 before adding 4 to it. Now, using your calculator, do the following calculation without writing down intermediate answers. In other words, use “chain operation” to do the following computations: 5.7 x 2.8 3.1 x 4.2 The answer should be 0.815789474… If you calculator shows 6.395789473… you have entered the operations incorrectly into your calculator. You must have entered the steps in this order: 3.1 x 4.2 ÷ (5.7 x 2.8) which is incorrect. The correct way to enter the operations is to either put parenthesis around the terms in the numerator and denominator ( ) ( ) = 5.7 x 2.8 3.1 x 4.2 or remember that 2.8 is in the denominator, so you need to press ÷ not X: 3.1 X 4.2 ÷ 5.7 ÷ 2.8

It is important you understand this sequence of operations because you will OFTEN be needing to do this type of calculations this semester..

Practice with this problem, using your calculator: 3.2 x 10³² x 5.1 x 10 ^-12 / 7.4 x10¹²

answer 2.205405 x 10⁻⁹ ?

Units can be handled just like algebraic terms

gallon/ (gallon/mile)= gallon* mile/gallon= mile