999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 as a fraction

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 as a fraction - solution and the full explanation with calculat

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What is 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 as a fraction?


To write 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 as a fraction you have to write 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 = 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999/1 = 1.0E+97/10 = 1.0E+98/100 = 1.0E+99/1000 = 1.0E+100/10000 = 1.0E+101/100000 = 1.0E+102/1000000 = 1.0E+103/10000000 = 1.0E+104/100000000 = 1.0E+105/1000000000 = 1.0E+106/10000000000 = 1.0E+107/100000000000 = 1.0E+108/1000000000000 = 1.0E+109/10000000000000 = 1.0E+110/100000000000000 = 1.0E+111/1000000000000000 = 1.0E+112/10000000000000000 = 1.0E+113/100000000000000000 = 1.0E+114/1000000000000000000 = 1.0E+115/1.0E+19 = 1.0E+116/1.0E+20 = 1.0E+117/1.0E+21 = 1.0E+118/1.0E+22 = 1.0E+119/1.0E+23 = 1.0E+120/1.0E+24 = 1.0E+121/1.0E+25 = 1.0E+122/1.0E+26 = 1.0E+123/1.0E+27 = 1.0E+124/1.0E+28 = 1.0E+125/1.0E+29 = 1.0E+126/1.0E+30 = 1.0E+127/1.0E+31 = 1.0E+128/1.0E+32 = 1.0E+129/1.0E+33 = 1.0E+130/1.0E+34 = 1.0E+131/1.0E+35 = 1.0E+132/1.0E+36 = 1.0E+133/1.0E+37 = 1.0E+134/1.0E+38 = 1.0E+135/1.0E+39 = 1.0E+136/1.0E+40 = 1.0E+137/1.0E+41 = 1.0E+138/1.0E+42 = 1.0E+139/1.0E+43 = 1.0E+140/1.0E+44 = 1.0E+141/1.0E+45 = 1.0E+142/1.0E+46 = 1.0E+143/1.0E+47 = 1.0E+144/1.0E+48 = 1.0E+145/1.0E+49 = 1.0E+146/1.0E+50 = 1.0E+147/1.0E+51 = 1.0E+148/1.0E+52 = 1.0E+149/1.0E+53 = 1.0E+150/1.0E+54 = 1.0E+151/1.0E+55 = 1.0E+152/1.0E+56 = 1.0E+153/1.0E+57 = 1.0E+154/1.0E+58 = 1.0E+155/1.0E+59 = 1.0E+156/1.0E+60 = 1.0E+157/1.0E+61 = 1.0E+158/1.0E+62 = 1.0E+159/1.0E+63 = 1.0E+160/1.0E+64 = 1.0E+161/1.0E+65 = 1.0E+162/1.0E+66 = 1.0E+163/1.0E+67 = 1.0E+164/1.0E+68 = 1.0E+165/1.0E+69 = 1.0E+166/1.0E+70 = 1.0E+167/1.0E+71 = 1.0E+168/1.0E+72 = 1.0E+169/1.0E+73 = 1.0E+170/1.0E+74 = 1.0E+171/1.0E+75 = 1.0E+172/1.0E+76 = 1.0E+173/1.0E+77 = 1.0E+174/1.0E+78 = 1.0E+175/1.0E+79 = 1.0E+176/1.0E+80 = 1.0E+177/1.0E+81 = 1.0E+178/1.0E+82 = 1.0E+179/1.0E+83 = 1.0E+180/1.0E+84 = 1.0E+181/1.0E+85 = 1.0E+182/1.0E+86 = 1.0E+183/1.0E+87 = 1.0E+184/1.0E+88 = 1.0E+185/1.0E+89 = 1.0E+186/1.0E+90 = 1.0E+187/1.0E+91 = 1.0E+188/1.0E+92 = 1.0E+189/1.0E+93 = 1.0E+190/1.0E+94 = 1.0E+191/1.0E+95 = 1.0E+192/1.0E+96 = 1.0E+193/1.0E+97 = 1.0E+194/1.0E+98 = 1.0E+195/1.0E+99

And finally we have:
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 as a fraction equals 1.0E+195/1.0E+99

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