{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["sbNRN","Calc_Rational","Relation to Power of 10"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":5,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"sbNRN","index":0,"n_rows":31,"n_cols":12,"rows_kept":31,"cut":false,"hidden":false,"merged":[[0,0,0,2],[0,3,0,4],[0,9,0,10],[18,0,18,2],[18,3,18,4],[18,9,18,10]]}
["Input",null,null,"Result",null,"Quality Measure",null,null,null,"Expected Result",null,"Quality Measure"]
["dFloat","lMaxDen","dMaxErr","pK","qK","Absolute Error","# of \"?\"","TEXT Representation","Comment","pK","qK","Result as expected?"]
[{"$f":"PI()","v":3.1415926535897931},1,null,{"$f":"IF(ISBLANK(C3),sbnrn(A3,B3),sbnrn(A3,B3,C3))","v":3},1,{"$f":"ABS(A3-D3/E3)","v":0.14159265358979312},1,{"$f":"TEXT(A3,REPT(\"?\",G3)&\"/\"&REPT(\"?\",G3))","v":"22/7"},null,3,1,{"$f":"AND(D3=J3,E3=K3)","v":true}]
[{"$f":"PI()","v":3.1415926535897931},10,null,{"$f":"IF(ISBLANK(C4),sbnrn(A4,B4),sbnrn(A4,B4,C4))","v":22},7,1.2644892673496777E-3,1,"22/7",null,22,7,true]
[{"$f":"PI()","v":3.1415926535897931},{"$f":"E6-1","v":112},{"$f":"F4","v":1.2644892673496777E-3},{"$f":"IF(ISBLANK(C5),sbnrn(A5,B5),sbnrn(A5,B5,C5))","v":333},106,8.3219627529107498E-5,3,"355/113",null,333,106,true]
[{"$f":"PI()","v":3.1415926535897931},1000,null,{"$f":"IF(ISBLANK(C6),sbnrn(A6,B6),sbnrn(A6,B6,C6))","v":355},113,2.667641894049666E-7,3,"355/113",null,355,113,true]
[{"$f":"PI()","v":3.1415926535897931},33214,{"$f":"F6","v":2.667641894049666E-7},{"$f":"IF(ISBLANK(C7),sbnrn(A7,B7),sbnrn(A7,B7,C7))","v":103993},33102,5.7789062424262738E-10,5,"312689/99532",null,103993,33102,true]
[{"$f":"PI()","v":3.1415926535897931},66316,{"$f":"F7","v":5.7789062424262738E-10},{"$f":"IF(ISBLANK(C8),sbnrn(A8,B8),sbnrn(A8,B8,C8))","v":104348},33215,3.3162805834763276E-10,5,"312689/99532",null,104348,33215,true]
[{"$f":"PI()","v":3.1415926535897931},99531,{"$f":"F8","v":3.3162805834763276E-10},{"$f":"IF(ISBLANK(C9),sbnrn(A9,B9),sbnrn(A9,B9,C9))","v":208341},66317,1.2235634727630895E-10,5,"312689/99532",null,208341,66317,true]
[{"$f":"PI()","v":3.1415926535897931},100000,null,{"$f":"IF(ISBLANK(C10),sbnrn(A10,B10),sbnrn(A10,B10,C10))","v":312689},99532,2.9143354396410359E-11,5,"312689/99532",null,312689,99532,true]
[{"$f":"PI()","v":3.1415926535897931},364912,{"$f":"F10","v":2.9143354396410359E-11},{"$f":"IF(ISBLANK(C11),sbnrn(A11,B11),sbnrn(A11,B11,C11))","v":833719},265381,8.7152507433074788E-12,6,"1146408/364913",null,833719,265381,true]
[{"$f":"PI()","v":3.1415926535897931},1360119,{"$f":"F11","v":8.7152507433074788E-12},{"$f":"IF(ISBLANK(C12),sbnrn(A12,B12),sbnrn(A12,B12,C12))","v":1146408},364913,1.6107115641261771E-12,6,"1146408/364913",null,1146408,364913,true]
[{"$f":"PI()","v":3.1415926535897931},1725032,{"$f":"F12","v":1.6107115641261771E-12},{"$f":"IF(ISBLANK(C13),sbnrn(A13,B13),sbnrn(A13,B13,C13))","v":4272943},1360120,4.0412118096355698E-13,7,"5419351/1725033",null,4272943,1360120,true]
[{"$f":"PI()","v":3.1415926535897931},25510581,{"$f":"F13","v":4.0412118096355698E-13},{"$f":"IF(ISBLANK(C14),sbnrn(A14,B14),sbnrn(A14,B14,C14))","v":5419351},1725033,2.2204460492503131E-14,7,"5419351/1725033",null,5419351,1725033,true]
[{"$f":"PI()","v":3.1415926535897931},78256778,{"$f":"F14","v":2.2204460492503131E-14},{"$f":"IF(ISBLANK(C15),sbnrn(A15,B15),sbnrn(A15,B15,C15))","v":80143857},25510582,4.4408920985006262E-16,8," 5419351/1725033 ","Accuracy limit of TEXT reached",80143857,25510582,true]
[{"$f":"PI()","v":3.1415926535897931},100000000,null,{"$f":"IF(ISBLANK(C16),sbnrn(A16,B16),sbnrn(A16,B16,C16))","v":245850922},78256779,0,8," 5419351/1725033 ","Accuracy limit of TEXT reached",245850922,78256779,true]
[]
[]
["Input",null,null,"Result",null,"Quality Measure",null,null,null,"Expected Result",null,"Quality Measure"]
["dFloat","lMaxDen","dMaxErr","pK","qK","Absolute Error","# of \"?\"","TEXT Representation","Comment","pK","qK","Result as expected?"]
[{"$f":"EXP(1)","v":2.7182818284590451},1,1,{"$f":"IF(ISBLANK(C21),sbnrn(A21,B21),sbnrn(A21,B21,C21))","v":2},1,{"$f":"ABS(A21-D21/E21)","v":0.71828182845904509},1,{"$f":"TEXT(A21,REPT(\"?\",G21)&\"/\"&REPT(\"?\",G21))","v":"19/7"},null,2,1,{"$f":"AND(D21=J21,E21=K21)","v":true}]
[{"$f":"EXP(1)","v":2.7182818284590451},10,null,{"$f":"IF(ISBLANK(C22),sbnrn(A22,B22),sbnrn(A22,B22,C22))","v":19},7,3.9961141733306782E-3,1,"19/7",null,19,7,true]
[2.7182818284590451,100,null,{"$f":"IF(ISBLANK(C23),sbnrn(A23,B23),sbnrn(A23,B23,C23))","v":193},71,2.8030695884417867E-5,2,"193/71",null,193,71,true]
[2.7182818284590451,1000,{"$f":"F23","v":2.8030695884417867E-5},{"$f":"IF(ISBLANK(C24),sbnrn(A24,B24),sbnrn(A24,B24,C24))","v":1457},536,1.7536305070287028E-6,3,"1457/536",null,1457,536,true]
[2.7182818284590451,5000,{"$f":"F24","v":1.7536305070287028E-6},{"$f":"IF(ISBLANK(C25),sbnrn(A25,B25),sbnrn(A25,B25,C25))","v":2721},1001,{"$f":"ABS(A25-D25/E25)","v":1.1017732681750658E-7},4,"25946/9545",null,2721,1001,true]
[2.7182818284590451,10000,{"$f":"F25","v":1.1017732681750658E-7},{"$f":"IF(ISBLANK(C26),sbnrn(A26,B26),sbnrn(A26,B26,C26))","v":25946},9545,5.515095491404054E-9,5,"49171/18089",null,25946,9545,true]
[2.7182818284590451,100000,{"$f":"F26","v":5.515095491404054E-9},{"$f":"IF(ISBLANK(C27),sbnrn(A27,B27),sbnrn(A27,B27,C27))","v":49171},18089,2.7665070234661471E-10,6,"1084483/398959",null,49171,18089,true]
[2.7182818284590451,1000000,null,{"$f":"IF(ISBLANK(C28),sbnrn(A28,B28),sbnrn(A28,B28,C28))","v":1084483},398959,4.8183679268731794E-13,7,"14665106/5394991",null,1084483,398959,true]
[2.7182818284590451,10000000,{"$f":"F28","v":4.8183679268731794E-13},{"$f":"IF(ISBLANK(C29),sbnrn(A29,B29),sbnrn(A29,B29,C29))","v":14665106},5394991,1.6875389974302379E-14,8,"14665106/5394991 ","Accuracy limit of TEXT reached",14665106,5394991,true]
[2.7182818284590451,100000000,{"$f":"F29","v":1.6875389974302379E-14},{"$f":"IF(ISBLANK(C30),sbnrn(A30,B30),sbnrn(A30,B30,C30))","v":28245729},10391023,8.8817841970012523E-16,9," 14665106/5394991  ","Accuracy limit of TEXT reached",28245729,10391023,true]
[2.7182818284590451,1000000000,{"$f":"F30","v":8.8817841970012523E-16},{"$f":"IF(ISBLANK(C31),sbnrn(A31,B31),sbnrn(A31,B31,C31))","v":2334068333},858655754,0,10,"  14665106/5394991   ","Accuracy limit of TEXT reached",2334068333,858655754,true]

{"sheet":"Calc_Rational","index":1,"n_rows":10,"n_cols":7,"rows_kept":10,"cut":false,"hidden":false,"merged":[[1,2,1,3],[1,4,1,5]]}
[null,"Max Error",0.1]
[null,null,"Original",null,"Shortened Fraction"]
[null,null,"Nominator","Denominator","Nominator","Denominator","Text"]
[null,"Input A",4,28,{"$f":"sbnrn(C4/D4,D4,MaxError)","v":1},7,{"$f":"IF(E4 = 0, \"0\", IF(ABS(QUOTIENT(E4,F4)) > 0, QUOTIENT(E4,F4) & IF(MOD(E4,F4) <> 0, CHOOSE(SIGN(QUOTIENT(E4,F4))+2,\" - \",\"\", \" + \") & MOD(E4,F4) & \" / \" & F4, \"\"), E4 & \" / \" & F4))","v":"1 / 7"}]
[null,"Input B",3,33,{"$f":"sbnrn(C5/D5,D5,MaxError)","v":1},11,{"$f":"IF(E5 = 0, \"0\", IF(ABS(QUOTIENT(E5,F5)) > 0, QUOTIENT(E5,F5) & IF(MOD(E5,F5) <> 0, CHOOSE(SIGN(QUOTIENT(E5,F5))+2,\" - \",\"\", \" + \") & MOD(E5,F5) & \" / \" & F5, \"\"), E5 & \" / \" & F5))","v":"1 / 11"}]
[]
[null,"Output A+B",{"$f":"NomA * DenomB + NomB * DenomA","v":216},{"$f":"DenomA * DenomB","v":924},{"$f":"sbnrn(C7/D7,D7,MaxError)","v":18},77,{"$f":"IF(E7 = 0, \"0\", IF(ABS(QUOTIENT(E7,F7)) > 0, QUOTIENT(E7,F7) & IF(MOD(E7,F7) <> 0, CHOOSE(SIGN(QUOTIENT(E7,F7))+2,\" - \",\"\", \" + \") & MOD(E7,F7) & \" / \" & F7, \"\"), E7 & \" / \" & F7))","v":"18 / 77"}]
[null,"Output A-B",{"$f":"NomA * DenomB - NomB * DenomA","v":48},{"$f":"DenomA * DenomB","v":924},{"$f":"sbnrn(C8/D8,D8,MaxError)","v":4},77,{"$f":"IF(E8 = 0, \"0\", IF(ABS(QUOTIENT(E8,F8)) > 0, QUOTIENT(E8,F8) & IF(MOD(E8,F8) <> 0, CHOOSE(SIGN(QUOTIENT(E8,F8))+2,\" - \",\"\", \" + \") & MOD(E8,F8) & \" / \" & F8, \"\"), E8 & \" / \" & F8))","v":"4 / 77"}]
[null,"Output A*B",{"$f":"NomA * NomB","v":12},{"$f":"DenomA * DenomB","v":924},{"$f":"sbnrn(C9/D9,D9,MaxError)","v":1},77,{"$f":"IF(E9 = 0, \"0\", IF(ABS(QUOTIENT(E9,F9)) > 0, QUOTIENT(E9,F9) & IF(MOD(E9,F9) <> 0, CHOOSE(SIGN(QUOTIENT(E9,F9))+2,\" - \",\"\", \" + \") & MOD(E9,F9) & \" / \" & F9, \"\"), E9 & \" / \" & F9))","v":"1 / 77"}]
[null,"Output A/B",{"$f":"NomA * DenomB","v":132},{"$f":"DenomA * NomB","v":84},{"$f":"sbnrn(C10/D10,D10,MaxError)","v":11},7,{"$f":"IF(E10 = 0, \"0\", IF(ABS(QUOTIENT(E10,F10)) > 0, QUOTIENT(E10,F10) & IF(MOD(E10,F10) <> 0, CHOOSE(SIGN(QUOTIENT(E10,F10))+2,\" - \",\"\", \" + \") & MOD(E10,F10) & \" / \" & F10, \"\"), E10 & \" / \" & F10))","v":"1 + 4 / 7"}]

{"sheet":"Relation to Power of 10","index":2,"n_rows":22,"n_cols":3,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
["Input","Output","Formula in B"]
[1E-14,{"$f":"IFERROR(--A2*10^(LEN(--A2)-SEARCH(\",\",--A2))&\":\"&10^(LEN(--A2)-SEARCH(\",\",--A2)),--A2&\":1\")","v":"1:100000000000000"},{"$f":"sbgetcell(B2,\"FormulaWOT\")","v":"=IFERROR(--A2*10^(LEN(--A2)-SEARCH(\",\",--A2))&\":\"&10^(LEN(--A2)-SEARCH(\",\",--A2)),--A2&\":1\")"}]
[1.0000000000000001E-5,{"$f":"IFERROR(--A3*10^(LEN(--A3)-SEARCH(\",\",--A3))&\":\"&10^(LEN(--A3)-SEARCH(\",\",--A3)),--A3&\":1\")","v":"1:100000"},{"$f":"sbgetcell(B3,\"FormulaWOT\")","v":"=IFERROR(--A3*10^(LEN(--A3)-SEARCH(\",\",--A3))&\":\"&10^(LEN(--A3)-SEARCH(\",\",--A3)),--A3&\":1\")"}]
[0.1,{"$f":"IFERROR(--A4*10^(LEN(--A4)-SEARCH(\",\",--A4))&\":\"&10^(LEN(--A4)-SEARCH(\",\",--A4)),--A4&\":1\")","v":"1:10"},{"$f":"sbgetcell(B4,\"FormulaWOT\")","v":"=IFERROR(--A4*10^(LEN(--A4)-SEARCH(\",\",--A4))&\":\"&10^(LEN(--A4)-SEARCH(\",\",--A4)),--A4&\":1\")"}]
[0.2,"2:10",{"$f":"sbgetcell(B5,\"FormulaWOT\")","v":"=IFERROR(--A5*10^(LEN(--A5)-SEARCH(\",\",--A5))&\":\"&10^(LEN(--A5)-SEARCH(\",\",--A5)),--A5&\":1\")"}]
[0.22,"22:100",{"$f":"sbgetcell(B6,\"FormulaWOT\")","v":"=IFERROR(--A6*10^(LEN(--A6)-SEARCH(\",\",--A6))&\":\"&10^(LEN(--A6)-SEARCH(\",\",--A6)),--A6&\":1\")"}]
[1.2339999999999999E-4,"1234:10000000",{"$f":"sbgetcell(B7,\"FormulaWOT\")","v":"=IFERROR(--A7*10^(LEN(--A7)-SEARCH(\",\",--A7))&\":\"&10^(LEN(--A7)-SEARCH(\",\",--A7)),--A7&\":1\")"}]
[0,"0:1",{"$f":"sbgetcell(B8,\"FormulaWOT\")","v":"=IFERROR(--A8*10^(LEN(--A8)-SEARCH(\",\",--A8))&\":\"&10^(LEN(--A8)-SEARCH(\",\",--A8)),--A8&\":1\")"}]
[1,"1:1",{"$f":"sbgetcell(B9,\"FormulaWOT\")","v":"=IFERROR(--A9*10^(LEN(--A9)-SEARCH(\",\",--A9))&\":\"&10^(LEN(--A9)-SEARCH(\",\",--A9)),--A9&\":1\")"}]
[10,"10:1",{"$f":"sbgetcell(B10,\"FormulaWOT\")","v":"=IFERROR(--A10*10^(LEN(--A10)-SEARCH(\",\",--A10))&\":\"&10^(LEN(--A10)-SEARCH(\",\",--A10)),--A10&\":1\")"}]
[100,"100:1",{"$f":"sbgetcell(B11,\"FormulaWOT\")","v":"=IFERROR(--A11*10^(LEN(--A11)-SEARCH(\",\",--A11))&\":\"&10^(LEN(--A11)-SEARCH(\",\",--A11)),--A11&\":1\")"}]
[{"$f":"PI()","v":3.1415926535897931},"314159265358979:100000000000000",{"$f":"sbgetcell(B12,\"FormulaWOT\")","v":"=IFERROR(--A12*10^(LEN(--A12)-SEARCH(\",\",--A12))&\":\"&10^(LEN(--A12)-SEARCH(\",\",--A12)),--A12&\":1\")"}]
[1.1000000000000001,"11:10",{"$f":"sbgetcell(B13,\"FormulaWOT\")","v":"=IFERROR(--A13*10^(LEN(--A13)-SEARCH(\",\",--A13))&\":\"&10^(LEN(--A13)-SEARCH(\",\",--A13)),--A13&\":1\")"}]
[12.12,"1212:100",{"$f":"sbgetcell(B14,\"FormulaWOT\")","v":"=IFERROR(--A14*10^(LEN(--A14)-SEARCH(\",\",--A14))&\":\"&10^(LEN(--A14)-SEARCH(\",\",--A14)),--A14&\":1\")"}]
[123.123,"123123:1000",{"$f":"sbgetcell(B15,\"FormulaWOT\")","v":"=IFERROR(--A15*10^(LEN(--A15)-SEARCH(\",\",--A15))&\":\"&10^(LEN(--A15)-SEARCH(\",\",--A15)),--A15&\":1\")"}]
[9.9999999999999997E+199,"1E+200:1",{"$f":"sbgetcell(B16,\"FormulaWOT\")","v":"=IFERROR(--A16*10^(LEN(--A16)-SEARCH(\",\",--A16))&\":\"&10^(LEN(--A16)-SEARCH(\",\",--A16)),--A16&\":1\")"}]
[9.9999999999999998E-201,"1E-200:1",{"$f":"sbgetcell(B17,\"FormulaWOT\")","v":"=IFERROR(--A17*10^(LEN(--A17)-SEARCH(\",\",--A17))&\":\"&10^(LEN(--A17)-SEARCH(\",\",--A17)),--A17&\":1\")"}]
[-0.1,"-1:10",{"$f":"sbgetcell(B18,\"FormulaWOT\")","v":"=IFERROR(--A18*10^(LEN(--A18)-SEARCH(\",\",--A18))&\":\"&10^(LEN(--A18)-SEARCH(\",\",--A18)),--A18&\":1\")"}]
[{"$f":"-PI()","v":-3.1415926535897931},"-314159265358979:100000000000000",{"$f":"sbgetcell(B19,\"FormulaWOT\")","v":"=IFERROR(--A19*10^(LEN(--A19)-SEARCH(\",\",--A19))&\":\"&10^(LEN(--A19)-SEARCH(\",\",--A19)),--A19&\":1\")"}]
[-123.123,"-123123:1000",{"$f":"sbgetcell(B20,\"FormulaWOT\")","v":"=IFERROR(--A20*10^(LEN(--A20)-SEARCH(\",\",--A20))&\":\"&10^(LEN(--A20)-SEARCH(\",\",--A20)),--A20&\":1\")"}]
[-12.12,"-1212:100",{"$f":"sbgetcell(B21,\"FormulaWOT\")","v":"=IFERROR(--A21*10^(LEN(--A21)-SEARCH(\",\",--A21))&\":\"&10^(LEN(--A21)-SEARCH(\",\",--A21)),--A21&\":1\")"}]
[-4.0000000000000003E-5,"-4:100000",{"$f":"sbgetcell(B22,\"FormulaWOT\")","v":"=IFERROR(--A22*10^(LEN(--A22)-SEARCH(\",\",--A22))&\":\"&10^(LEN(--A22)-SEARCH(\",\",--A22)),--A22&\":1\")"}]