Download Lesson 1 - Arithmetic

College Algebra to Calculus and the TI-83
Lesson #1
Arithmetic
I. Basic Arithmetic
Order of the operations:
1. Operations within symbols of inclusion, parenthesis, brackets, braces and
bars.
2. Powers (exponents) and roots.
3. Multiplication and division as they appear from left to right.
4. Addition and subtraction.
3
Exercise 1. Compute 33  14  21 18  6  3
 33  14^3  21 + 18  6  3 ENTER
answer: 4321
II. Arithmetic with fractions and decimals
Converting terminating or repeating decimals to fractions
The following process converts rational numbers in decimal notation to
fractional notation.
 MATH
1
 ENTER
5
1 6
,
,
32 6 7
Exercise 2: Convert the fractions




ON
532 ENTER
16 ENTER
67 ENTER
Exercise 3: Add

ans.: 0.15625
ans.: 0.1666666667
ans.: 0.8571428571
2 4

3 5
2  3  4  5 MATH
Exercise 4. Simplify:

to decimals
1
ENTER
5 2 4 2 5
   
3 5 7 3 4
Answer:
5  3 + (2  5)  (4  7) - (2  3)  (5  4) MATH 1 ENTER
answer: 23 / 15
-6-
22
15
Exercise 5: Compute 2 
2
3
5
1
3
 ON
 2  (2  3)  (5  1  3) ENTER
Ans.: 2.125
Exercise 6. Give the answer to exercise 6 in fractional form.




ON
2  (2  3)  (5  1  3)
MATH 1
ENTER
Answer: 17/8
Exercise 7: convert the repeating decimal 0.77777777…. to a fraction.



0.7777777777777 (as many 7’s as possible)
MATH 1
ENTER
answer: 7/9
Exercise 8. Convert the repeating decimal 0.254545454... to a fraction



0.254545454545454545454
MATH 1
ENTER
Answer: 14/55
Exercise 9: convert 0.354

0.35444444444444 MATH 1 ENTER
answer:
319
900
III. Arithmetic with irrational numbers (radicals and transcendental
numbers)
1. To compute 3 n , use MATH 4
x
n ) ENTER
2. To compute n : the x root of a number, use the following
procedure,
x MATH 5 n ENTER
3. To raise to a power use ^
4. The irrational number π is given in float mode as 3.141592654
5. The irrational number e is given in float mode as 2.718281828
x
6. To obtain e use 2nd e (fifth row and fifth column) or 2nd e
e^(1) ENTER
answer: 2.718281828
-7-
Exercise 10: Compute
3

MODE  (Float)


MATH
4
317 , round answer to 5 decimal places.
317 )
5
(to select 5 decimal places)
ENTER
ENTER
2nd Quit
answer: 6.81846
4 5
Exercise 11: Compute
(5 decimal places)
13


ON
(-) 4 MATH
5
5  13
3
Exercise 12 : Compute




ON
MATH 4
17)  5
ENTER
5
ENTER
answer: -0.11503
17
(5 decimal places)
23
MATH 5 23
answer: 1.37342
2 5  33 5
Exercise 13. Compute
. Round answer to the nearest thousandth.
5 4 3


ON
MODE  (Float)  3 (to select 3 decimal places) ENTER

( 2 2nd

ENTER
( 5 ) - 3 MATH 4 5) )  ( 5 2nd
answer: -0.094
2nd Quit
( 4 ) -3)
3
17 
 (3 decimal places)
Exercise 14: Calculate 
180 

(17180)^3
ENTER
answer: 0.026
IV. Scientific Notation
2nd EE
To work in scientific notation go to MODE and select Sci and Float or
select any desired number of decimal places)
When the calculator is in Sci mode and you ENTER a number in standard
notation, the output appears in scientific mode.
-8-
Exercise 15. Convert the numbers 3456000000 and 0.0007832 to scientific notation
 MODE  Sci ENTER Float ENTER
2nd Quit
 3456000000 ENTER
answer: 3.456E9
 0.0007832
ENTER
answer: 7.832E-4



Exercise 16. Compute 2.5 105 3.42 103 . Also, give answer in standard notation.
 ON
 MODE  Sci ENTER  Float ENTER 2nd Quit
 2.5 2nd EE 5  3.42 2nd EE (-) 3 ENTER
answer: 8.55E2
 MODE  Normal ENTER 2nd QUIT ENTER
answer: 855
2.5 10 3.42 10  in SCI MODE
2.58 10 
3
5
Exercise 17. Compute


4 2
MODE  Sci ENTER Float ENTER 2nd QUIT
(2.5 2nd EE 5)(3.42 2nd EE-3) (2.58 2nd EE-4)^2 ENTER
answer: 1.284478096E10
3
5  4 2
Exercise 18. Calculate 3     (3)( 5) . Give answer in decimal and fractional form.
2
9
 MODE  Normal ENTER  Float ENTER 2nd QUIT
 52^(-3)+(49)^(32) - (-3)(-5) ENTER ans.: 25.2962963
 MATH 1 ENTER
answer: 683/27
Note: the key - (above the  sign) is used for subtraction
the key (-) (to the left of ENTER) is used to express negative numbers.
Exercise 19. Evaluate the expression x 5  x 3  3x 2  5 x  13 x=5, x=-3
and x=-2.15
 (5)^5 – (5)^3+3(5)^2+5(5)-13 ENTER
answer: 3087
 (-3)^5 - (-3)^3 + 3(-3)^2 + 5(-3) – 13
ENTER
answer: -217

(  2.15)^5   2.153  3 2.15^2  5 2.15  13 ENTER answer: -45.88426344
n
 1
Exercise 20. Find the value of the expression 1   for n  10 6 , n  109 , n  1012
 n
 MODE Normal Float
 2nd EE 6 STO ALPHA N ENTER
 (1+1N)^N ENTER answer: 2.718280469
 2nd EE 9 STO N ENTER
 2nd ENTRY (as many times as needed until (1+1N)^N appears, ENTER
answer: 2.718281827
 2nd EE 12 STO N ENTER
 2nd ENTRY (as many times as needed until (1+1N)^N appears ENTER
answer: 2.718281828
-9-
Exercise 21. Suppose the total cost of manufacturing q units of a certain product is given
4
3
2
by the function C(q) = q  5q  50q  400q  250
a) Determine the cost of manufacturing 15 units, C(15)
 ON
 15^4 - 5*15^3 +50*15^2 +400*15 +250 ENTER answer: $51250
b) Determine the cost of manufacturing the 15th unit, that is, C(15) - C(14)

2nd ANS - ( 14^4 -5*14^3 +50*14^2 +400*14 +250) ENTER
answer: $ 10904
Exercise 22. A certain machine bought for $25000 depreciates linearly so that its value
after 12 years will be $1000. If (t, y) represents the value y of the machine after t years,
using the fact that (0, 25000) and (12, 1000) are points of the depreciation line, we
obtain the equation of linear depreciation to be y = -2000t + 25000
Determine the value of the machine after 7 years.
 ON
 -2000*7 + 25000 ENTER
answer: $11000
n
 1 
Exercise 23. Find the value of 1   for a) n=250, b) n=1000,
 n 
c)





n=1000000
d) n=100,000,000
ON
(1 + 1250)^250
ENTER
answer: 2.712865123
(1 + 11000)^1000
ENTER
answer: 2.716923932
nd
(1 + 12 EE6)^2ndEE6 ENTER
answer: 2.718280469
nd
(1 + 12 EE8)^2ndEE8 ENTER
answer: 2.718281815
2
x  5x  6
Exercise 24. Find the value of
when a) x=0.99875
3
x 1
b) x =1.000003

(0.99875^2 + 5*0.99875 -6)  (0.99875^3 -1)

(1.000003^2 + 5*1.000003-6)  (1.000003^3 -1) ENTER
answer: 2.333327333
-10-
ENTER
answer: 2.335835244