2. Calculator Input
2 5
Mathematics expressions such 8 or 3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software.
3. Calculator Input
2 5
Mathematics expressions such 8 or
3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC.
4. Calculator Input
2 5
Mathematics expressions such 8 or
3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC. For example, the book–format 3 is “3/4” in the
4
BASIC format. (All calculator–inputs through out this course
will be in “quoted boldface”.)
5. Calculator Input
2 5
Mathematics expressions such 8 or
3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC. For example, the book–format 3 is “3/4” in the
4
BASIC format. (All calculator–inputs through out this course
will be in “quoted boldface”.)
In the BASIC–format, addition and subtraction are “+” and “–”,
6. Calculator Input
2 5
Mathematics expressions such 8 or
3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC. For example, the book–format 3 is “3/4” in the
4
BASIC format. (All calculator–inputs through out this course
will be in “quoted boldface”.)
In the BASIC–format, addition and subtraction are “+” and “–”,
multiplication operation is “ * ” (or shift + 8),
7. Calculator Input
2 5
Mathematics expressions such 8 or
3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC. For example, the book–format 3 is “3/4” in the
4
BASIC format. (All calculator–inputs through out this course
will be in “quoted boldface”.)
In the BASIC–format, addition and subtraction are “+” and “–”,
multiplication operation is “ * ” (or shift + 8),
the division operation is “ / ”,
8. Calculator Input
2 5
Mathematics expressions such 8 or
3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC. For example, the book–format 3 is “3/4” in the
4
BASIC format. (All calculator–inputs through out this course
will be in “quoted boldface”.)
In the BASIC–format, addition and subtraction are “+” and “–”,
multiplication operation is “ * ” (or shift + 8),
the division operation is “ / ”,
and the power operation is “ ^ ” (or shift + 6).
9. Calculator Input
2 5
Mathematics expressions such 8 or3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC. For example, the book–format 3 is “3/4” in the
4
BASIC format. (All calculator–inputs through out this course
will be in “quoted boldface”.)
In the BASIC–format, addition and subtraction are “+” and “–”,
multiplication operation is “ * ” (or shift + 8),
the division operation is “ / ”,
and the power operation is “ ^ ” (or shift + 6).
So the BASIC–input for 32 is “3^2” and for 4 x 32, it’s “4*3^2”.
10. Calculator Input
2 5
Mathematics expressions such 8 or3
3 + x2 that appeared in
books can’t be keyboarded directly “as is” into calculators,
smart phone apps or computer software. While there is no
standard input method that would work for all of them, most
keyboard mathematics–input methods are similar to the
BASIC–input method which is used in the computer language
BASIC. For example, the book–format 3 is “3/4” in the
4
BASIC format. (All calculator–inputs through out this course
will be in “quoted boldface”.)
In the BASIC–format, addition and subtraction are “+” and “–”,
multiplication operation is “ * ” (or shift + 8),
the division operation is “ / ”,
and the power operation is “ ^ ” (or shift + 6).
So the BASIC–input for 32 is “3^2” and for 4 x 32, it’s “4*3^2”.
Finally, we also use “+" and “–” as signs however this may or
may not be the case depending on the calculator or software.
12. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
13. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?).
14. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
15. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
16. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
17. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Missing a quantity Missing a “ ) ”
for the subtraction
operation
18. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Missing a quantity Missing a “ ) ” Missing a quantity
for the subtraction for the multiplication
operation operation
19. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Missing a quantity Missing a “ ) ” Missing a quantity
for the subtraction for the multiplication
operation operation
Following are some of the common syntax errors.
20. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Missing a quantity Missing a “ ) ” Missing a quantity
for the subtraction for the multiplication
operation operation
Following are some of the common syntax errors.
* It take two quantities to perform +, --, *, / and ^.
21. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Missing a quantity Missing a “ ) ” Missing a quantity
for the subtraction for the multiplication
operation operation
Following are some of the common syntax errors.
* It take two quantities to perform +, --, *, / and ^.
Inputs such as “6*”, “23 /”, or “7^” generate error–messages.
22. Power Equations and Calculator Input
Syntax
The word “syntax” refers to the rules for recognizable input.
If we enter “5 + ” in the calculator, press “enter”, we get an
error message (5 plus what?). Such an error where the input
is incomplete or gibberish is called a “syntax error”.
Example A. Find the syntax error in each of the following
expressions.
a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Missing a quantity Missing a “ ) ” Missing a quantity
for the subtraction for the multiplication
operation operation
Following are some of the common syntax errors.
* It take two quantities to perform +, --, *, / and ^.
Inputs such as “6*”, “23/”, or “7^” generate error–messages.
Note that “+6” is OK but “6+” generates an error.
23. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it.
24. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
25. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
26. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
The machine always tell us when we made a syntax error with
an error message.
27. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
The machine always tell us when we made a syntax error with
an error message. However another type of mistake that occurs
often for which there is no warning and is difficult to catch are
the “miscommunications “.
28. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
The machine always tell us when we made a syntax error with
an error message. However another type of mistake that occurs
often for which there is no warning and is difficult to catch are
the “miscommunications “.
Semantics
29. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
The machine always tell us when we made a syntax error with
an error message. However another type of mistake that occurs
often for which there is no warning and is difficult to catch are
the “miscommunications “.
Semantics
Semantics are the rules for interpreting the "meaning“ of
syntactically correct expressions.
30. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
The machine always tell us when we made a syntax error with
an error message. However another type of mistake that occurs
often for which there is no warning and is difficult to catch are
the “miscommunications “.
Semantics
Semantics are the rules for interpreting the "meaning“ of
syntactically correct expressions. The semantics for BASIC–
format inputs are the same as the rules for order of operations
PEMDAS.
31. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
The machine always tell us when we made a syntax error with
an error message. However another type of mistake that occurs
often for which there is no warning and is difficult to catch are
the “miscommunications “.
Semantics
Semantics are the rules for interpreting the "meaning“ of
syntactically correct expressions. The semantics for BASIC–
format inputs are the same as the rules for order of operations
PEMDAS. A semantic input mistake is a mistake where we
mean to execute one set of calculations without realizing that
the input is interpreted differently by the machine.
32. Power Equations and Calculator Input
* For every left parentheses “( ” opened , there must be a
right parentheses “)” that closes it. Hence the number of “( ”
should be the same the number of “)” in the inputs.
* Symbols such as [ ] or { } may have different meanings.
The machine always tell us when we made a syntax error with
an error message. However another type of mistake that occurs
often for which there is no warning and is difficult to catch are
the “miscommunications “.
Semantics
Semantics are the rules for interpreting the "meaning“ of
syntactically correct expressions. The semantics for BASIC–
format inputs are the same as the rules for order of operations
PEMDAS. A semantic input mistake is a mistake where we
mean to execute one set of calculations without realizing that
the input is interpreted differently by the machine. Here are
some examples of similar but different inputs.
33. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
c. Find “–2–4^(1/2)/2” with and without the calculator.
d. Write the BASIC input of 2–√4 . Find the answer.
2
34. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
–43 = –64 .
It’s 3 3
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
c. Find “–2–4^(1/2)/2” with and without the calculator.
d. Write the BASIC input of 2–√4 . Find the answer.
2
35. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
–43 = –64 . The input yields –64/3 = –21.33…
It’s 3 3
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
c. Find “–2–4^(1/2)/2” with and without the calculator.
d. Write the BASIC input of 2–√4 . Find the answer.
2
36. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
–43 = –64 . The input yields –64/3 = –21.33…
It’s 3 3
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
2
The BASIC input of –8 is “–8^(2/3)”.
3
c. Find “–2–4^(1/2)/2” with and without the calculator.
d. Write the BASIC input of 2–√4 . Find the answer.
2
37. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
–43 = –64 . The input yields –64/3 = –21.33…
It’s 3 3
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
2
The BASIC input of –8 is “–8^(2/3)”. The answer is –4.
3
c. Find “–2–4^(1/2)/2” with and without the calculator.
The input yields –3 because it’s –2 –√4 .
2
d. Write the BASIC input of 2–√4 . Find the answer.
2
38. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
–43 = –64 . The input yields –64/3 = –21.33…
It’s 3 3
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
2
The BASIC input of –8 is “–8^(2/3)”. The answer is –4.
3
c. Find “–2–4^(1/2)/2” with and without the calculator.
The input yields –3 because it’s –2 –√4 .
2
d. Write the BASIC input of 2–√4 . Find the answer.
2
The correct BASIC format is “(–2–4^(1/2))/2”.
39. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
–43 = –64 . The input yields –64/3 = –21.33…
It’s 3 3
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
2
The BASIC input of –8 is “–8^(2/3)”. The answer is –4.
3
c. Find “–2–4^(1/2)/2” with and without the calculator.
The input yields –3 because it’s –2 –√4 .
2
d. Write the BASIC input of 2–√4 . Find the answer.
2
The correct BASIC format is “(–2–4^(1/2))/2”. The answer is 0.
40. Power Equations and Calculator Input
Example B.
a. Find “–8^2/3” with and without the calculator .
–43 = –64 . The input yields –64/3 = –21.33…
It’s 3 3
2
b. Write –8 in the BASIC input, find the answer with and
3
without the calculator.
2
The BASIC input of –8 is “–8^(2/3)”. The answer is –4.
3
c. Find “–2–4^(1/2)/2” with and without the calculator.
The input yields –3 because it’s –2 –√4 .
2
d. Write the BASIC input of 2–√4 . Find the answer.
2
The correct BASIC format is “(–2–4^(1/2))/2”. The answer is 0.
When in doubt, insert ( )’s to specify the order of
operations.
41. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations.
42. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
43. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
44. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits.
45. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
46. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
47. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
0.001234 ≈ 0.00123.
48. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
0.001234 ≈ 0.00123.
Example C. Solve for x and find the approximate solution.
a. 3x2/3 – 7 = 1
49. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
0.001234 ≈ 0.00123.
Example C. Solve for x and find the approximate solution.
a. 3x2/3 – 7 = 1
3x2/3 = 8
50. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
0.001234 ≈ 0.00123.
Example C. Solve for x and find the approximate solution.
a. 3x2/3 – 7 = 1
3x2/3 = 8
x2/3 = 8/3
51. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
0.001234 ≈ 0.00123.
Example C. Solve for x and find the approximate solution.
a. 3x2/3 – 7 = 1
3x2/3 = 8
x2/3 = 8/3
x = (8/3) 3/2
52. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
0.001234 ≈ 0.00123.
Example C. Solve for x and find the approximate solution.
a. 3x2/3 – 7 = 1
3x2/3 = 8
x2/3 = 8/3
x = (8/3) 3/2 The exact answer
53. Power Equations and Calculator Input
We use calculators to obtain approximate decimal answers for
irrational solutions of power equations. The accuracy of the
approximation required depends on the application.
For example, if the problem is about money, then we round off
at to the penny, i.e. the 2nd position after the decimal point.
However all other decimal answers in this course are rounded
off to three significant digits. To obtain this,
start from the 1st nonzero digit,
count and round off at the third digit.
For example, 12.35 ≈ 12.4
0.001234 ≈ 0.00123.
Example C. Solve for x and find the approximate solution.
a. 3x2/3 – 7 = 1
3x2/3 = 8
x2/3 = 8/3
x = (8/3) 3/2 The exact answer
≈ 4.35 The approx. answer
