Well, honey, let me break it down for you. A decimal that repeats like 0.64 is considered rational because it can be expressed as a fraction. In this case, 0.64 repeating is the same as 64/99, making it a rational number. So, there you have it - rational all the way.
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It is a rational number because it can be expressed as a fraction in the form of 64/99
7000000 + 60000 + 4000 + 80 = 7064080 7 000 000 .... 60 000 ...... 4 000 ........... 80 + ----------- 7 064 080
288 000, 001, 002, 003, 004, 005, 006, 010, 011, 012, 013, 014, 015, 016, 020, 021, 022, 023, 024, 025, 026, 030, 031, 032, 033, 034, 035, 036, 040, 041, 042, 043, 044, 045, 046, 050, 051, 052, 053, 054, 055, 056, 060, 061, 062, 063, 064, 065, 066 x 6 Unless you mean all numbers in the string must be unique, excluding numbers like 000 and 001, then it's 180 or 012, 013, 014, 015, 016, 021, 023, 024, 025, 026, 031, 032, 034, 035, 036, 041, 042, 043, 045, 046, 051, 052, 053, 054, 056, 061, 062, 063, 064, 065 x 6