Sunday, May 15, 2016

Fraction Approximation on Graphing Calculators Comparisons

Fraction Approximation on Graphing Calculators Comparisons

 Advanced calculators and calculator apps sometimes give the ability for the user to convert answers to fractions.  For rational numbers, the fractional conversions are precise and easy.  However, for irrational numbers, different calculators use different algorithms.  I am going to use three calculators to compare fractional answers:

TI-Nspire CAS iOS App:  Fractional Approximations

* TI-NSpire CAS iOS App:  this should be similar to the TI-Nspire CAS handheld calculators, x→approxFraction(5.E-14)

* Casio Classpad fx-CP400:  fractional approximation used by tofrac(approx(x))

* HP Prime (firmware 10077), pressing [a b/c] after the number is entered

Square Root of 2, √2
Decimal Approximation
1.41421356237
TI-NSpire CAS
3,880,899/2,744,210
Casio Classpad fx-CP400
13,250,218/9,369,319
HP Prime
114,243/80,782

Square Root of 3, √3
Approximation
1.73205080757
TI-NSpire CAS
3,650,401/2,107,560
Casio Classpad fx-CP400
3,650,401/2,107,560
HP Prime
191,861/110,771

Square Root of 5, √5
Approximation
2.2360679775
TI-NSpire CAS
3,940,598/1,762,289
Casio Classpad fx-CP400
16,692,641/7,465,176
HP Prime
219,602/98,209

Euler’s Number, e
Approximation
2.71828182846
TI-NSpire CAS
14,665,106/5,394,991
Casio Classpad fx-CP400
14,665,106/5,394,991
HP Prime
219,602/98,209

The Constant Pi, π
Approximation
3.14159265359
TI-NSpire CAS
5,149,351/1,725,033
Casio Classpad fx-CP400
69,305,155/22,060,516
HP Prime
312,689/99,532

The Constant Pi, π^2
Approximation
9.86960440109
TI-NSpire CAS
26,140,802/2,648,617
Casio Classpad fx-CP400
26,140,802/2,648,617
HP Prime
12,59,401/127,604

The Golden Ratio, Φ = (1 + √5)/2
Approximation
1.61803398875
TI-NSpire CAS
5,702,887/3,524,578
Casio Classpad fx-CP400
5,702,887/3,524,578
HP Prime
121,393/75,025

The Zeta of 3, ζ(3) ≈ 1.20205693015959428539
Approximation
1.20205690316
TI-NSpire CAS
2,721,755/2,264,248
Casio Classpad fx-CP400
2,721,755/2,264,248
HP Prime
927,328/771,451


This blog is property of Edward Shore, 2016

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