Statistics

Problem Statement for "BestApproximationDiv2"

Problem Statement

Elly is not a big fan of mathematical constants. Most of them are infinite, and therefore hard to memorize. Fractions, on the other hand, are often easier to remember and can provide good approximations. For example, 22/7 = 3.1428... is one way to approximate Pi. Unfortunately, it's only accurate to 2 places after the decimal point, so it doesn't help at all. A slightly better example is 355/113 = 3.14159292... which is correct up to 6 digits after the decimal point.

Elly understands that working with infinite decimal fractions is going to be very difficult, so she first wants to find a good way to approximate floating point numbers with decimal representations that are finite. Your task is to help her in this mission. You will be given a String number containing the decimal representation of a non-negative fraction strictly less than 1 (possibly with trailing zeros). More precisely, number will be formatted "0.dd...d" (quotes for clarity) where each d is a decimal digit ('0'-'9') and the number of d's is between 1 and 48, inclusive.

Given a fraction F = A/B, where 0 <= A < B, its quality of approximation with respect to number is calculated as follows:
  • Let S be the decimal fraction (infinite or finite) representation of F.
  • Let N be the number of digits after the decimal point in number. If number has trailing zeros, all of them are considered to be significant and are counted towards N.
  • If S is infinite or the number of digits after the decimal point in S is greater than N, only consider the first N decimals after the decimal point in S. Truncate the rest of the digits without performing any kind of rounding.
  • If the number of digits after the decimal point in S is less than N, append trailing zeroes to the right side until there are exactly N digits after the decimal point.
  • The quality of approximation is the number of digits in the longest common prefix of S and number. The longest common prefix of two numbers is the longest string which is a prefix of the decimal representations of both numbers with no extra leading zeroes. For example, "3.14" is the longest common prefix of 3.1428 and 3.1415.
Elly doesn't like long approximations either, so you are only allowed to use fractions where the denominator is less than or equal to maxDen. Find an approximation F = A/B of number such that 1 <= B <= maxDen, 0 <= A < B, and the quality of approximation is maximized. Return a String formatted "A/B has X exact digits" (quotes for clarity) where A/B is the approximation you have found and X is its quality. If there are several such approximations, choose the one with the smallest denominator among all of them. If there is still a tie, choose the one among those with the smallest numerator.

Definition

Class:
BestApproximationDiv2
Method:
findFraction
Parameters:
int, String
Returns:
String
Method signature:
String findFraction(int maxDen, String number)
(be sure your method is public)

Constraints

  • maxDen will be between 1 and 100,000, inclusive.
  • number will contain between 3 and 50 characters, inclusive.
  • number will consist of a digit '0', followed by a period ('.'), followed by one or more digits ('0'-'9').

Examples

  1. 42

    "0.141592658"

    Returns: "1/7 has 3 exact digits"

    3 plus the current approximation yields an approximation of Pi.

  2. 3

    "0.1337"

    Returns: "0/1 has 1 exact digits"

    Not a lot of options here.

  3. 80000

    "0.1234567891011121314151617181920"

    Returns: "10/81 has 8 exact digits"

  4. 1000

    "0.42"

    Returns: "3/7 has 3 exact digits"

    This one can be represented in more than one way. Be sure to choose the one with the lowest denominator. Note that 21/50 is an even more accurate approximation (it is, in fact, exact), but it has the same number of matching digits (all three) and has a greater denominator.

  5. 100

    "0.420"

    Returns: "21/50 has 4 exact digits"

    All trailing zeros in number are significant.

  6. 115

    "0.141592658"

    Returns: "16/113 has 7 exact digits"

    A better approximation for the decimal part of Pi.

  7. 512

    "0.000000000000"

    Returns: "0/1 has 13 exact digits"

  8. 1000

    "0.272727272727272727272727272727272727272727272727"

    Returns: "3/11 has 49 exact digits"

  9. 100000

    "0.99979980180378574789041150739232438957325345"

    Returns: "99881/99901 has 32 exact digits"

  10. 99999

    "0.00001"

    Returns: "1/50001 has 6 exact digits"

  11. 100000

    "0.00001"

    Returns: "1/50001 has 6 exact digits"

  12. 100000

    "0.999999999999"

    Returns: "99999/100000 has 6 exact digits"

  13. 100000

    "0.000099999999999999999999999999999999999999999999"

    Returns: "1/10001 has 9 exact digits"

  14. 100000

    "0.000009999999999999999999999999999999999999999999"

    Returns: "0/1 has 6 exact digits"

  15. 9172

    "0.618927954312334"

    Returns: "739/1194 has 8 exact digits"

  16. 13016

    "0.13893446066184"

    Returns: "1609/11581 has 9 exact digits"

  17. 98926

    "0.165754120014607177"

    Returns: "5873/35432 has 10 exact digits"

  18. 38912

    "0.6406189841439880877"

    Returns: "8321/12989 has 9 exact digits"

  19. 35131

    "0.74380880681"

    Returns: "19763/26570 has 10 exact digits"

  20. 17422

    "0.618211976295"

    Returns: "7081/11454 has 9 exact digits"

  21. 58425

    "0.4912508393967997693576658254416163355328253"

    Returns: "10977/22345 has 10 exact digits"

  22. 38467

    "0.75812574444429307787303825"

    Returns: "27360/36089 has 10 exact digits"

  23. 57549

    "0.05310675004549564821683148492070607056"

    Returns: "1847/34779 has 9 exact digits"

  24. 29588

    "0.11173004830129"

    Returns: "1043/9335 has 10 exact digits"

  25. 96723

    "0.0356667677191627276513995926532444279237"

    Returns: "1528/42841 has 10 exact digits"

  26. 75536

    "0.65281031552217482363035280722591085079053"

    Returns: "33717/51649 has 10 exact digits"

  27. 43779

    "0.32412908745"

    Returns: "7583/23395 has 11 exact digits"

  28. 89529

    "0.481435526892959"

    Returns: "30653/63670 has 10 exact digits"

  29. 8171

    "0.9182801848609300876356583948397"

    Returns: "3225/3512 has 9 exact digits"

  30. 48997

    "0.566144626825510151760"

    Returns: "22485/39716 has 11 exact digits"

  31. 25785

    "0.39219823402319898913514253892870148193597980"

    Returns: "6505/16586 has 9 exact digits"

  32. 24510

    "0.81033848015413735856908936069789415666667"

    Returns: "4405/5436 has 9 exact digits"

  33. 55122

    "0.603624588121"

    Returns: "10625/17602 has 11 exact digits"

  34. 27491

    "0.20892820552767878160958900072552148646"

    Returns: "4039/19332 has 9 exact digits"

  35. 80251

    "0.64419557473408815232466629049311995556059"

    Returns: "11792/18305 has 10 exact digits"

  36. 70197

    "0.4212779554034122982278583944"

    Returns: "6593/15650 has 10 exact digits"

  37. 19371

    "0.4679347881638"

    Returns: "861/1840 has 9 exact digits"

  38. 55854

    "0.2012770241037395972028670818303620284183"

    Returns: "7597/37744 has 11 exact digits"

  39. 79772

    "0.972282944827258473"

    Returns: "23573/24245 has 10 exact digits"

  40. 76080

    "0.0407590512098917330"

    Returns: "2193/53804 has 10 exact digits"

  41. 87842

    "0.62214326054"

    Returns: "7704/12383 has 10 exact digits"

  42. 52802

    "0.8639453823948513281646779641926315970261762"

    Returns: "29991/34714 has 10 exact digits"

  43. 80980

    "0.0117591817"

    Returns: "576/48983 has 11 exact digits"

  44. 19897

    "0.5649843253832706801195363153403179035291261701"

    Returns: "5586/9887 has 9 exact digits"

  45. 47434

    "0.8780956900135580177467074121835714"

    Returns: "36981/42115 has 10 exact digits"

  46. 47730

    "0.126633008138"

    Returns: "2433/19213 has 10 exact digits"

  47. 27110

    "0.5206728006"

    Returns: "5541/10642 has 9 exact digits"

  48. 17827

    "0.8887400599530995111233972330484392490574"

    Returns: "10616/11945 has 9 exact digits"

  49. 7402

    "0.1577941785788"

    Returns: "578/3663 has 8 exact digits"

  50. 8517

    "0.92842758409443584103340675"

    Returns: "5993/6455 has 8 exact digits"

  51. 48298

    "0.37658789771650132605744906119042197093331356959"

    Returns: "2757/7321 has 10 exact digits"

  52. 32413

    "0.025607209543256088157579"

    Returns: "233/9099 has 11 exact digits"

  53. 68919

    "0.21335290485733030321108187289230282558124988271"

    Returns: "9884/46327 has 10 exact digits"

  54. 98584

    "0.7198832933283402012"

    Returns: "33309/46270 has 10 exact digits"

  55. 99238

    "0.929130819202475810071693037304323"

    Returns: "40931/44053 has 10 exact digits"

  56. 93370

    "0.794980018508928085147361680865710283556"

    Returns: "17705/22271 has 10 exact digits"

  57. 15278

    "0.14145763463"

    Returns: "1314/9289 has 9 exact digits"

  58. 81395

    "0.6200651619735006518272452258698"

    Returns: "21125/34069 has 10 exact digits"

  59. 25240

    "0.7852729763159895495252230872837541829689"

    Returns: "6228/7931 has 9 exact digits"

  60. 69275

    "0.4352915567902319878"

    Returns: "17998/41347 has 10 exact digits"

  61. 98617

    "0.0286814764987386280980"

    Returns: "2018/70359 has 11 exact digits"

  62. 98083

    "0.201038733145612191804774119810"

    Returns: "14206/70663 has 12 exact digits"

  63. 57270

    "0.32978011"

    Returns: "6404/19419 has 9 exact digits"

  64. 24763

    "0.3091876840379622730730736467401244"

    Returns: "1336/4321 has 9 exact digits"

  65. 4907

    "0.0395711003318866479448557569568547357671687"

    Returns: "155/3917 has 44 exact digits"

  66. 41477

    "0.97424025591379745769845946628504082835"

    Returns: "11573/11879 has 39 exact digits"

  67. 11910

    "0.6210866057019903"

    Returns: "5773/9295 has 17 exact digits"

  68. 27441

    "0.6524317912218268"

    Returns: "550/843 has 17 exact digits"

  69. 44336

    "0.96422494125273478648407"

    Returns: "23799/24682 has 24 exact digits"

  70. 57214

    "0.894353369763205828"

    Returns: "491/549 has 19 exact digits"

  71. 33476

    "0.21199119911991199119911991199119"

    Returns: "1927/9090 has 33 exact digits"

  72. 79581

    "0.9109475267087478799111748352013428686331765"

    Returns: "52098/57191 has 44 exact digits"

  73. 73372

    "0.2176248108925869894"

    Returns: "2877/13220 has 20 exact digits"

  74. 53660

    "0.62094155844155844155844155844155"

    Returns: "765/1232 has 33 exact digits"

  75. 21494

    "0.686157117278424350940017905"

    Returns: "12263/17872 has 28 exact digits"

  76. 87056

    "0.47009345794392"

    Returns: "503/1070 has 15 exact digits"

  77. 74811

    "0.3210181580848931260343581"

    Returns: "13772/42901 has 26 exact digits"

  78. 44372

    "0.5918419052444894"

    Returns: "2336/3947 has 17 exact digits"

  79. 3415

    "0.1873767258382642998027613412228796844181459"

    Returns: "95/507 has 44 exact digits"

  80. 94278

    "0.33965632"

    Returns: "1522/4481 has 9 exact digits"

  81. 59923

    "0.13319661071833342328242214906"

    Returns: "2468/18529 has 30 exact digits"

  82. 34618

    "0.936594202898550724637681"

    Returns: "517/552 has 25 exact digits"

  83. 82162

    "0.567176560374290738958755"

    Returns: "17093/30137 has 25 exact digits"

  84. 63217

    "0.2695081967213"

    Returns: "411/1525 has 14 exact digits"

  85. 24689

    "0.5195467183418"

    Returns: "12333/23738 has 14 exact digits"

  86. 79173

    "0.98250056342882899603611247365141652636184062255"

    Returns: "74111/75431 has 48 exact digits"

  87. 70587

    "0.59505530253741054001301236174365647364996"

    Returns: "4573/7685 has 42 exact digits"

  88. 13180

    "0.73997821350762527233115468409586056"

    Returns: "6793/9180 has 36 exact digits"

  89. 36081

    "0.0752759675488761803431"

    Returns: "566/7519 has 23 exact digits"

  90. 50188

    "0.7273240105697"

    Returns: "24497/33681 has 14 exact digits"

  91. 27875

    "0.798645013450234133705290425425924080"

    Returns: "8016/10037 has 37 exact digits"

  92. 65469

    "0.704744525547445255474452554744525547445"

    Returns: "1931/2740 has 40 exact digits"

  93. 12099

    "0.3366159355416293643688451208594449"

    Returns: "376/1117 has 35 exact digits"

  94. 27810

    "0.8070713809206137424949966644429619746497665110"

    Returns: "6049/7495 has 47 exact digits"

  95. 55554

    "0.398797734459154244414329"

    Returns: "11477/28779 has 25 exact digits"

  96. 76250

    "0.900650075"

    Returns: "13716/15229 has 10 exact digits"

  97. 6732

    "0.705340699815837937384898710865561694290"

    Returns: "383/543 has 40 exact digits"

  98. 51863

    "0.259480696"

    Returns: "1519/5854 has 10 exact digits"

  99. 37241

    "0.13618587531631009"

    Returns: "592/4347 has 18 exact digits"

  100. 68961

    "0.5211327272134780200084726431"

    Returns: "15992/30687 has 29 exact digits"

  101. 90254

    "0.318529141071466792"

    Returns: "14882/46721 has 19 exact digits"

  102. 80270

    "0.4997191565588329057428688537033382417682510"

    Returns: "32918/65873 has 44 exact digits"

  103. 24828

    "0.65424979817783415984"

    Returns: "5673/8671 has 21 exact digits"

  104. 90368

    "0.77611137172659289"

    Returns: "56251/72478 has 18 exact digits"

  105. 99977

    "0.00058286134235501324108919045627906387400058"

    Returns: "46/78921 has 45 exact digits"

  106. 78041

    "0.58433079434167573449401523394994"

    Returns: "537/919 has 33 exact digits"

  107. 52549

    "0.82138526826311003334"

    Returns: "10839/13196 has 21 exact digits"

  108. 8726

    "0.10144927536231884057971014492"

    Returns: "7/69 has 30 exact digits"

  109. 55255

    "0.0355531971345184399044839479"

    Returns: "134/3769 has 29 exact digits"

  110. 87473

    "0.4873304782298358315488936473"

    Returns: "2731/5604 has 29 exact digits"

  111. 81767

    "0.30067047016199558572439928372"

    Returns: "7220/24013 has 30 exact digits"

  112. 27640

    "0.427052785923753665689149560117302052785923"

    Returns: "1165/2728 has 43 exact digits"

  113. 87295

    "0.9467016605259173270075203149447332559430676828"

    Returns: "18757/19813 has 47 exact digits"

  114. 48498

    "0.32833353017597731372741"

    Returns: "2780/8467 has 17 exact digits"

  115. 44559

    "0.19457615637700793497193728436810528353009483259"

    Returns: "8043/41336 has 26 exact digits"

  116. 12575

    "0.46418402205844323765192655805534005689164"

    Returns: "1957/4216 has 8 exact digits"

  117. 81449

    "0.30790927253496298037372194137373369373"

    Returns: "2620/8509 has 28 exact digits"

  118. 4675

    "0.182266009852216748768472906403940886699507379"

    Returns: "37/203 has 44 exact digits"

  119. 71759

    "0.570346996695"

    Returns: "27647/48474 has 9 exact digits"

  120. 36635

    "0.646241124"

    Returns: "17201/26617 has 10 exact digits"

  121. 93850

    "0.0457983771145647091184146237106312749277"

    Returns: "333/7271 has 24 exact digits"

  122. 88064

    "0.841890367989215672566734500771"

    Returns: "64951/77149 has 18 exact digits"

  123. 53299

    "0.223230876432331990328"

    Returns: "11533/51664 has 18 exact digits"

  124. 42727

    "0.4131731821"

    Returns: "5263/12738 has 10 exact digits"

  125. 84127

    "0.040621714962"

    Returns: "541/13318 has 11 exact digits"

  126. 29247

    "0.330873644893867998815705566183838935957"

    Returns: "3632/10977 has 15 exact digits"

  127. 54200

    "0.638610885171694309853139654135870"

    Returns: "18058/28277 has 20 exact digits"

  128. 80581

    "0.5212874312487268282735976777347728661641882"

    Returns: "2559/4909 has 21 exact digits"

  129. 2758

    "0.792682926829268292682926829268292672"

    Returns: "65/82 has 35 exact digits"

  130. 65085

    "0.800731780299764919996966709638280"

    Returns: "45082/56301 has 10 exact digits"

  131. 12588

    "0.473855030652722683014785430941208896501"

    Returns: "1314/2773 has 32 exact digits"

  132. 45023

    "0.341266512895785279932899969031243447263577269"

    Returns: "3255/9538 has 26 exact digits"

  133. 43846

    "0.410276438760452533202164289227742252"

    Returns: "12081/29446 has 10 exact digits"

  134. 67667

    "0.587024377166274104287547155358855209590011"

    Returns: "30655/52221 has 31 exact digits"

  135. 89397

    "0.628603032077558722102834478495"

    Returns: "9661/15369 has 22 exact digits"

  136. 87516

    "0.448562084533077387935018307205473922007749457"

    Returns: "25237/56262 has 31 exact digits"

  137. 7378

    "0.819248826291069812206"

    Returns: "349/426 has 14 exact digits"

  138. 21726

    "0.2888446215039442231075697"

    Returns: "145/502 has 11 exact digits"

  139. 52943

    "0.9705317114420243433696348494554772581"

    Returns: "1515/1561 has 9 exact digits"

  140. 87474

    "0.61636409480584972264246081780131114"

    Returns: "4889/7932 has 25 exact digits"

  141. 7312

    "0.35064578180818906292937610225336630942"

    Returns: "1276/3639 has 25 exact digits"

  142. 13885

    "0.7087496438021"

    Returns: "7590/10709 has 9 exact digits"

  143. 63781

    "0.092734733756717147044455300"

    Returns: "1921/20715 has 10 exact digits"

  144. 81871

    "0.594873150105708245233"

    Returns: "2251/3784 has 20 exact digits"

  145. 3102

    "0.7668918918908"

    Returns: "227/296 has 12 exact digits"

  146. 26880

    "0.6339525000520878548485111554822467228"

    Returns: "6621/10444 has 9 exact digits"

  147. 94216

    "0.3979401507393479847538723542291"

    Returns: "4907/12331 has 10 exact digits"

  148. 44801

    "0.45505778966472432449135543031808195"

    Returns: "4764/10469 has 16 exact digits"

  149. 48301

    "0.885265903736115775930663076405250"

    Returns: "21041/23768 has 17 exact digits"

  150. 44169

    "0.949226755"

    Returns: "10189/10734 has 9 exact digits"

  151. 31197

    "0.9353734217847206"

    Returns: "4371/4673 has 16 exact digits"

  152. 69996

    "0.91565106743955888590404251378481549554644422"

    Returns: "32382/35365 has 22 exact digits"

  153. 85587

    "0.20299298519085869056897895"

    Returns: "6511/32075 has 13 exact digits"

  154. 4029

    "0.59782607695652173913043"

    Returns: "55/92 has 8 exact digits"

  155. 3440

    "0.575727676269018253576714356191415885545140601"

    Returns: "1167/2027 has 10 exact digits"

  156. 31867

    "0.94760857842120545898531"

    Returns: "22844/24107 has 20 exact digits"

  157. 41800

    "0.92095996718060920994153"

    Returns: "26939/29251 has 23 exact digits"

  158. 10960

    "0.6936538056082648113007644317942230655703141471"

    Returns: "3290/4743 has 22 exact digits"

  159. 94241

    "0.42815716437043398075"

    Returns: "34402/80349 has 18 exact digits"

  160. 31956

    "0.1376730165619154508043396932285821"

    Returns: "3183/23120 has 9 exact digits"

  161. 71539

    "0.960522386886894752557715577884"

    Returns: "61119/63631 has 27 exact digits"

  162. 25651

    "0.4440343262971"

    Returns: "4812/10837 has 10 exact digits"

  163. 60924

    "0.4876482624390730780344850531499010197461447607"

    Returns: "29314/60113 has 18 exact digits"

  164. 100

    "0.909"

    Returns: "10/11 has 4 exact digits"

  165. 99991

    "0.999979998599901993139519766383646855279869590871"

    Returns: "49995/49996 has 10 exact digits"

  166. 100000

    "0.314159265358979323846264338327950288419716939937"

    Returns: "71/226 has 8 exact digits"

  167. 45234

    "0.2341235423123234234"

    Returns: "4859/20754 has 10 exact digits"

  168. 97567

    "0.6876098797632487238476328437629876"

    Returns: "23858/34697 has 10 exact digits"

  169. 99999

    "0.599067439767013706591197847890228232979542625952"

    Returns: "17473/29167 has 10 exact digits"

  170. 100000

    "0.4200"

    Returns: "21/50 has 5 exact digits"

  171. 100000

    "0.0000000083458734652746"

    Returns: "0/1 has 9 exact digits"

  172. 10000

    "0.98493849148959862134119850850968234150985123095"

    Returns: "4643/4714 has 8 exact digits"

  173. 100000

    "0.43489090314967484371609146097601981960471390493"

    Returns: "4365/10037 has 10 exact digits"

  174. 100000

    "0.141592658"

    Returns: "4783/33780 has 10 exact digits"

  175. 99999

    "0.1234567899998777776666666666"

    Returns: "10/81 has 8 exact digits"

  176. 98

    "0.1337"

    Returns: "2/15 has 4 exact digits"

  177. 7

    "0.141592658"

    Returns: "1/7 has 3 exact digits"

  178. 100000

    "0.448305799387298197748392834724989823468"

    Returns: "18073/40314 has 10 exact digits"

  179. 100000

    "0.123456789"

    Returns: "10/81 has 8 exact digits"

  180. 100000

    "0.141592658979323846264338326950288419716931418591"

    Returns: "4783/33780 has 10 exact digits"

  181. 100

    "0.0000000067860687"

    Returns: "0/1 has 9 exact digits"

  182. 89329

    "0.10290340007656086753"

    Returns: "6089/59172 has 10 exact digits"

  183. 97567

    "0.68760987976324872398757832998476328437629876"

    Returns: "23858/34697 has 10 exact digits"

  184. 100000

    "0.222222222222222222222222222222222222222222222222"

    Returns: "2/9 has 49 exact digits"

  185. 100000

    "0.123456789123456789123456789123456789"

    Returns: "10/81 has 8 exact digits"

  186. 100000

    "0.123213213213123123345435354"

    Returns: "4103/33300 has 13 exact digits"

  187. 100000

    "0.4567876545678765456787652345687906758495"

    Returns: "13705/30003 has 25 exact digits"

  188. 20

    "0.333333333333333333333333333333333333333333333333"

    Returns: "1/3 has 49 exact digits"

  189. 100000

    "0.254654864646546784321346546546546456"

    Returns: "21117/82924 has 11 exact digits"

  190. 99999

    "0.45689894566568897312323156448897897895"

    Returns: "6583/14408 has 10 exact digits"

  191. 100000

    "0.12345678910111213134343434151617181920"

    Returns: "10/81 has 8 exact digits"

  192. 99999

    "0.123637461672645389056432785432123456783929239596"

    Returns: "12284/99355 has 11 exact digits"

  193. 100000

    "0.197367625619736762561973676256197367625677"

    Returns: "9792/49613 has 10 exact digits"

  194. 100000

    "0.000000000000000000000000000000000000000000000001"

    Returns: "0/1 has 48 exact digits"

  195. 100000

    "0.032794242021506118715156117852149748865146624782"

    Returns: "1900/57937 has 49 exact digits"

  196. 100000

    "0.948576017495810295639485064104982057391749059938"

    Returns: "33074/34867 has 11 exact digits"

  197. 100

    "0.0"

    Returns: "0/1 has 2 exact digits"

  198. 100000

    "0.1234567891234567899876543223456789765213567"

    Returns: "10/81 has 8 exact digits"

  199. 100000

    "0.784829027240752875472985719875981759187985719869"

    Returns: "5256/6697 has 10 exact digits"

  200. 100000

    "0.618726487192648172648716348971648761284361183643"

    Returns: "22203/35885 has 10 exact digits"

  201. 99999

    "0.123456789012345678901234567890123456000"

    Returns: "10/81 has 8 exact digits"

  202. 100000

    "0.123451234512345123451234512345123451234512345123"

    Returns: "4115/33333 has 49 exact digits"

  203. 99999

    "0.98765987659876598765987659876599"

    Returns: "98765/99999 has 32 exact digits"

  204. 100000

    "0.999999999999999999999999999999999999999999999999"

    Returns: "99999/100000 has 6 exact digits"

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