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CCZOO 37.2. A.) Number systems
1.) Decimal system Review of Mathematics outline decimal notation, numbers described in words, exponential notation 2.) Binary system
3 ) Roman numerals B. ) Basic calculations _. ‘ 1.) Performing calculations without a calculator (principles of arithmetic) 2 .) Calculations with negative numbers
3.) Calculations with scientific notation
4.) Calculations with fractions
5.) Calculations with radicals . C.) Algebra (Calms. show with rme'd’QQ“ [‘L *1" "h l.) Rearrangements to solve for the unknown variable "* “"¢“" 31”““5 2.) Mathematical classiﬁcation of the types of equations 3.) Quadratic equations
4.) Ratio and proportion (see Grater“... M‘l'CS. 11: WM} 5 .) Use of several equations to derive the one needed to solve a problem Iv 5| to] sol 6 VII 100- ! l 11 2 HI 3 1V 4 V 5 V1 7 V111 Performing Calculations Without-a Calculator ‘ (when calculator fails or is not with you, or to check a calculation) Ardkmehe [vet-4‘ tomc- 14415 sLm—ut all 15¢ 91a; glean-‘1" he.“ Addition oi" Numbers with Decimals To add numbers with decimals we
use the same procedure as that used when adding whole numbers. but we always line up the decimal points in the same column. For example, add
8.21 + 143.1 + 0.325 8.21 AM ‘1‘ 143.] “MW“ 4‘ + 0.325 Ari-closet _ ,__..
151.635 SUW" When adding numbers that express units of measurement, we must be certain that the numbers added together represent the same units. For example. what is_‘ the total length of three pieces of glass tubing: 10.0 cm, I25 mm, and 8.4 em? if we
simply add the numbers, we obtain a value of [43.4, but we are not certain what the unit of measurement is. To add these lengths correctly, ﬁrst change 125 mm to ‘ 12.5 cm. Now all the lengths are expressed in the same units and can be added. 10.0 cm
8.4 cm 30.9 cm Subtraction of Numbers with Decimals To subtract numbers containing : decimals, we use the same procedure as for subtracting whole numbers, but we always line up the decimal Eints in the same column. For example, subtract
20.60 from 182.49. ' 182.49 Minus-Ht
_ 2050 - Sauna her-J.
ﬂ Multiplication of Numbers with Decimals To multiply two or more numbers together that contain decimals, we ﬁrst multiply as if they were whole numbers. [ Then, to locate the decimal point in the product, we add together the number of digits to the right of the decimal in all the numbers multiplied together. The pro- duct should have this same number of digits to the right of the decimal point.
Multiply 2.05 x 2.05 (total of four digits to the right of the decimal): 205 Matttpln‘ u“).
x205 Multiplied“ (.0? mﬂ'f'lle")
. 4100 soul MEOOO 81X 9X10 50 .LX 60 LXX 70 LXXXSO XC 90
CCC 300 CD400 D 500 DCGOO DCC 700 DCCCSOO CM 900 MCDXCVI 1496 MDCCCLXXXHI 1883 MCMIL 1949 MCMLXXW 1974 Roman numerals are a different type of numbering system.
_ .- . as They do NOT use arable numerals,
they do NOT use a zero, and they do NOT use a base system
where each digit represents that
number of powers of the base. Roman numerals are used by chemists 1C 99 C 1001
XM99O M1000. For this course, you must know the
Roman numerals for 1 to 3 (Le. Ito VIII). Symbols: for Multiplication: 3 x49 = 3% = 3%) = (31%) = for Division: ' a i b =% = 21/1) == a-(bl‘1 ()er Here are more examples: Cu-F “411391: ail": an) 14.25 x 6.01 x 0.75 = 64.231875 (six digits to the right of the decimal)
39.26 x 60 = 2355.60 (two digits to the right of the decimal) [Nate: When at least one of the numbers that is multiplied is a measurement, the
answer must be adjusted to contain the correct number of signiﬁcant ﬁgures. (See
Section % on signiﬁcant ﬁgures.]] Division of Numbers with Decimals To divide numbers containing deci-
mals, we ﬁrst relocate the decimal points of the numerator and denominator by
moving them to the right as many places as needed to make the denominator a
whole number. (Move the decimal of both the numerator and the denominator
the same amount and in the same direction.) For example, 136.94 1369.4 Numoitw
4,1 = 41 Dentin-“mesa? The decimal point adjustment in this example is equivalent to multiplying both 1 - numerator and denominator by 10. Now we carry out the division normally,l ' locating the decimal point immediately above its position in the dividend. 33.4 0. 441 441 00,53 ‘ Quotievd‘
41l1369.4 ' 7 a m = 2625l44.1000 Donowlnuzaeaa
123 26 25 2525 2625
£4 21000 [Note: When at least one of the numbers in the division is a measurement, the 3
answer must be adjusted to contain the correct number of signiﬁcant ﬁgures-(See 3
Section” on signiﬁcant ﬁgures.” The foregoing examples are merely guides to the principles used in
performing the various mathematical operations illustrated. There are, no doubt,
shortcuts and other methods, and the student will discover these with experience.
Every student of chemistry should learn to use a scientiﬁc electronic calcula- . tor for solving mathematical problems. The use of a calculator will save many 3 hours of doing tedious longhand calculations. 'Al'ter solving a problem, the student should check for errors and evaluate the answer to see if it is logical and consistent with the data given. - Mar»; 5 Him ‘ 4,2025 (four digits to the right olthe decimal) “Hum .. G‘lst- “Him diet-5'] are 'm 'Ge—ew-l ‘1“th gulf-n5" writes) for the oxidation state in chemical names. D. l Logarithms ' ' _ Roman numerals- -an addition system (place largest values on left add the values to find the number)
Note that this is sometimes arsubtt'active system when one smaller symbol precedes a larger. ...
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- Fall '08