let\'s translate to decimal like this:
2∙30+2∙3-1+2∙3-2+2∙3-3+2∙3-4+2∙3-5+2∙3-6+2∙3-7+2∙3-8+2∙3-9+2∙3-10+2∙3-11+2∙3-12+2∙3-13+2∙3-14+2∙3-15+2∙3-16+2∙3-17+2∙3-18+2∙3-19+2∙3-20+2∙3-21+2∙3-22+2∙3-23 = 2∙1+2∙0.33333333333333+2∙0.11111111111111+2∙0.037037037037037+2∙0.012345679012346+2∙0.0041152263374486+2∙0.0013717421124829+2∙0.00045724737082762+2∙0.00015241579027587+2∙5.0805263425291E-5+2∙1.693508780843E-5+2∙5.6450292694768E-6+2∙1.8816764231589E-6+2∙6.2722547438631E-7+2∙2.0907515812877E-7+2∙6.9691719376256E-8+2∙2.3230573125419E-8+2∙7.7435243751396E-9+2∙2.5811747917132E-9+2∙8.6039159723773E-10+2∙2.8679719907924E-10+2∙9.5599066359748E-11+2∙3.1866355453249E-11+2∙1.0622118484416E-11 = 2+0.66666666666667+0.22222222222222+0.074074074074074+0.024691358024691+0.0082304526748971+0.0027434842249657+0.00091449474165524+0.00030483158055175+0.00010161052685058+3.3870175616861E-5+1.1290058538954E-5+3.7633528463178E-6+1.2544509487726E-6+4.1815031625754E-7+1.3938343875251E-7+4.6461146250838E-8+1.5487048750279E-8+5.1623495834264E-9+1.7207831944755E-9+5.7359439815849E-10+1.911981327195E-10+6.3732710906499E-11+2.1244236968833E-11 = 2.9999999999893810
got It: 2.222222222222222222222223 =2.9999999999893810
Translate the number 2.9999999999893810 в 101.00000000000000000000357500 - false like this:
the Fractional part of the number is multiplied by the base of the new number system:
 |
| 0. | 99999999998938*101.00000000000000000000357500 |
| 100 | .0*101.00000000000000000000357500 |
| 100 | .0*101.00000000000000000000357500 |
| 100 | .99999*101.00000000000000000000357500 |
| 100 | .99889*101.00000000000000000000357500 |
| 100 | .88838*101.00000000000000000000357500 |
| 89 | .72664*101.00000000000000000000357500 |
| 73 | .39109*101.00000000000000000000357500 |
| 39 | .4996*101.00000000000000000000357500 |
| 50 | .45965*101.00000000000000000000357500 |
| 46 | .42515*101.00000000000000000000357500 |
the result of the conversion was:
2.9999999999893810 = 2.1001001001001008973395046101.00000000000000000000357500
the Final answer: 2.222222222222222222222223 = 2.1001001001001008973395046101.00000000000000000000357500