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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