Casio fx-9750GIII: Effects of Rounding
How Accurate?
The program ROUNDS compare true results against the true results in one of five calculations:
1. A × B × C
2. A × B ÷ C
3. √(A^2 + B^2 - C^2)
4. A ÷ B ÷ C
5. (A + 1 ÷ B)^C
The rounded result is calculated after rounding after each step.
For example: A × B × C
True result:
T = A × B × C
Rounded Result:
R = round(A × B)
R = round(R × C)
The absolute error percentage is calculated.
Casio fx-9750GIII Program: ROUNDS
"2022-11-23 EWS"
"EFFECTS OF ROUNDING"
"# OF PLACES"?→N
"A"?→A
"B"?→B
"C"?→C
Menu "SELECT OPERATION",
"A×B×C",A
"A×B÷C",B
"√(A^2 + B^2 - C^2)",C
"A÷B÷C",D
"(A+1÷B)^C",E
Lbl A
RndFix(A×B,N)→R
RndFix(R×C,N)→R
A×B×C→T
Goto 1
Lbl B
RndFix(A×B,N)→R
RndFix(R÷C,N)→R
A×B÷C→T
Goto 1
Lbl C
RndFix(A²+B²,N)→R
RndFix(√(R-C²),N)→R
√(A²+B²- C²)→T
Goto 1
Lbl D
RndFix(A÷B,N)→R
RndFix(R÷C,N)→R
A÷B÷C→T
Goto 1
Lbl E
RndFix(A+1÷B,N)→R
RndFix(R^C,N)→R
(A+1÷B)^C→T
Goto 1
Lbl 1
RndFix(100×Abs (R-T)÷T,5)→E
ClrText
Locate 1,3,"ROUNDED:"
Locate 9,3,R
Locate 1,4,"ACTUAL:"
Locate 9,4,T
Locate 1,5,"ERROR%:"
Locate 9,5
Example:
Let A = 13.946, B = 11.9765, C = π^3/4
Round to 2 decimal places (N = 2)
1. A × B × C
Rounded: 1294.67
Actual: 1294.700174
Error: 2.33*10^-3 %
2. A × B ÷ C
Rounded: 21.55
Actual: 21.54715585
Error: 0.0132%
3. √(A^2 + B^2 - C^2)
Rounded: 16.67
Actual: 16.66855254
Error: 8.68*10^-3 %
4. A ÷ B ÷ C
Rounded: 0.15
Actual: 0.1502208155
Error: 0.14699%
5. (A + 1 ÷ B)^C
Rounded: 778927217
Actual: 778710708.2
Error: 0.0278%
Enjoy,
Eddie
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