let\'s translate to decimal like this:
1∙100+9∙10-1+9∙10-2+9∙10-3+9∙10-4+9∙10-5+9∙10-6+9∙10-7+9∙10-8+9∙10-9+9∙10-10+9∙10-11+9∙10-12+9∙10-13+9∙10-14+9∙10-15+9∙10-16+9∙10-17+9∙10-18+9∙10-19+9∙10-20+9∙10-21+9∙10-22+9∙10-23+9∙10-24 = 1∙1+9∙0.1+9∙0.01+9∙0.001+9∙0.0001+9∙1.0E-5+9∙1.0E-6+9∙1.0E-7+9∙1.0E-8+9∙1.0E-9+9∙1.0E-10+9∙1.0E-11+9∙1.0E-12+9∙1.0E-13+9∙1.0E-14+9∙1.0E-15+9∙1.0E-16+9∙1.0E-17+9∙1.0E-18+9∙1.0E-19+9∙1.0E-20+9∙1.0E-21+9∙1.0E-22+9∙1.0E-23+9∙1.0E-24 = 1+0.9+0.09+0.009+0.0009+9.0E-5+9.0E-6+9.0E-7+9.0E-8+9.0E-9+9.0E-10+9.0E-11+9.0E-12+9.0E-13+9.0E-14+9.0E-15+9.0E-16+9.0E-17+9.0E-18+9.0E-19+9.0E-20+9.0E-21+9.0E-22+9.0E-23+9.0E-24 = 1.110
got It: 1.99999999999999999999999910 =1.110
Translate the number 1.110 в 11.00000000000001 - false like this:
the Fractional part of the number is multiplied by the base of the new number system:
 |
| 0. | 1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
| 1 | .1*11.00000000000001 |
the result of the conversion was:
1.110 = 1.111111111111.00000000000001
the Final answer: 1.99999999999999999999999910 = 1.111111111111.00000000000001