let\'s translate to decimal like this:
3∙11.000000000+10∙11.00000000-1+10∙11.00000000-2+10∙11.00000000-3+10∙11.00000000-4+10∙11.00000000-5+10∙11.00000000-6+10∙11.00000000-7+10∙11.00000000-8+10∙11.00000000-9+10∙11.00000000-10+10∙11.00000000-11+10∙11.00000000-12+10∙11.00000000-13+10∙11.00000000-14 = 3∙1+10∙0.090909090909091+10∙0.0082644628099174+10∙0.00075131480090158+10∙6.8301345536507E-5+10∙6.2092132305916E-6+10∙5.6447393005378E-7+10∙5.1315811823071E-8+10∙4.6650738020973E-9+10∙4.2409761837248E-10+10∙3.8554328942953E-11+10∙3.5049389948139E-12+10∙3.1863081771036E-13+10∙2.8966437973669E-14+10∙2.6333125430608E-15 = 3+0.90909090909091+0.082644628099174+0.0075131480090158+0.00068301345536507+6.2092132305916E-5+5.6447393005378E-6+5.1315811823071E-7+4.6650738020973E-8+4.2409761837248E-9+3.8554328942953E-10+3.5049389948139E-11+3.1863081771036E-12+2.8966437973669E-13+2.6333125430608E-14 = 3.110
got It: 3.aaaaaaaaaaaaaa11.00000000 =3.110
Translate the number 3.110 в 4.00000000 - false like this:
the Fractional part of the number is multiplied by the base of the new number system:
 |
| 0. | 1*4.00000000 |
| 0 | .4*4.00000000 |
| 1 | .6*4.00000000 |
| 2 | .4*4.00000000 |
| 1 | .6*4.00000000 |
| 2 | .4*4.00000000 |
| 1 | .6*4.00000000 |
| 2 | .4*4.00000000 |
| 1 | .6*4.00000000 |
| 2 | .4*4.00000000 |
| 1 | .6*4.00000000 |
the result of the conversion was:
3.110 = 3.01212121214.00000000
the Final answer: 3.aaaaaaaaaaaaaa11.00000000 = 3.01212121214.00000000