REG x : input

REG 00 : index
REG 01~21 : work memory (continued fraction)
REG 22 : input value 
REG 23 : accumulator
REG 24 : work memory
FLAG00 : terminate approximation

LASTx : input value
REG t : input value
REG z : error
REG y : numerator
REG x : denominator

Fractional approximation using continued fraction	recompose and calculate error
00 { 138-Byte Prgm } 01 LBL "Frac" 02 CF 00 03 ABS 04 STO 22 05 STO 23 06 1.021 07 STO 00 08 CLχ 09 χ<>y 10 LBL B 11 IP 12 STO IND 00 13 χ≠0? 14 XEQ C 15 RCL 23 16 RCL- IND 00 17 χ=0? 18 SF 00 19 FS?C 00 20 GTO E 21 1/χ 22 STO 23 23 ISG 00 24 GTO B 25 LBL E 26 R↓ 27 RCL 22 28 ABS 29 CLχ 30 LASTχ 31 R↓ 32 RTN	33 LBL C 34 RCL 00 35 IP 36 χ<> 00 37 STO 24 38 0 39 1 40 LBL D 41 ENTER 42 ENTER 43 RCL IND 00 44 × 45 R↑ 46 + 47 DSE 00 48 GTO D 49 ABS 50 χ<>y 51 ENTER 52 ENTER 53 LASTχ 54 ÷ 55 RCL× 22 56 1 57 - 58 χ<> 24 59 STO 00 60 CLχ 61 2E-12 62 RCL 24 63 ABS 64 χ<y? 65 SF 00 66 CLχ 67 RCL 24 68 CLA 69 ARCL ST χ 70 "LF" 71 R↑ 72 AIP 73 "/" 74 R↑ 75 AIP 76 PROMPT 77 RTN 78 END

DISP SCI 3
π XEQ FRAC

4.720E-2 1/3

-4.023E-4 22/7

2.649E-5 333/106

-8.491E-8 355/113

1.800E-10 103993/33102

-1.060E-10 104348/33215

4.000E-11 208341/66317

-9.000E-12 312689/99532

0.000E0 833719/265381

Note: Simple continued fraction expression of π, to 12 digits accuracy.

Franctional approximation of π
Fractional approximation program for the HP-15C
Fractional approximation program for the HP-32sII
Fractional approximation program for the HP-35s
Find the nearest fraction in the E24 numbers

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