Here is a table of the first 64 negative powers of two (from 2-1 to 2-64), shown in decimals:
| n | 2n |
|---|---|
| -1 | 0.5 |
| -2 | 0.25 |
| -3 | 0.125 |
| -4 | 0.0625 |
| -5 | 0.03125 |
| -6 | 0.015625 |
| -7 | 0.0078125 |
| -8 | 0.00390625 |
| -9 | 0.001953125 |
| -10 | 0.0009765625 |
| -11 | 0.00048828125 |
| -12 | 0.000244140625 |
| -13 | 0.0001220703125 |
| -14 | 0.00006103515625 |
| -15 | 0.000030517578125 |
| -16 | 0.0000152587890625 |
| -17 | 0.00000762939453125 |
| -18 | 0.000003814697265625 |
| -19 | 0.0000019073486328125 |
| -20 | 0.00000095367431640625 |
| -21 | 0.000000476837158203125 |
| -22 | 0.0000002384185791015625 |
| -23 | 0.00000011920928955078125 |
| -24 | 0.000000059604644775390625 |
| -25 | 0.0000000298023223876953125 |
| -26 | 0.00000001490116119384765625 |
| -27 | 0.000000007450580596923828125 |
| -28 | 0.0000000037252902984619140625 |
| -29 | 0.00000000186264514923095703125 |
| -30 | 0.000000000931322574615478515625 |
| -31 | 0.0000000004656612873077392578125 |
| -32 | 0.00000000023283064365386962890625 |
| -33 | 0.000000000116415321826934814453125 |
| -34 | 0.0000000000582076609134674072265625 |
| -35 | 0.00000000002910383045673370361328125 |
| -36 | 0.000000000014551915228366851806640625 |
| -37 | 0.0000000000072759576141834259033203125 |
| -38 | 0.00000000000363797880709171295166015625 |
| -39 | 0.000000000001818989403545856475830078125 |
| -40 | 0.0000000000009094947017729282379150390625 |
| -41 | 0.00000000000045474735088646411895751953125 |
| -42 | 0.000000000000227373675443232059478759765625 |
| -43 | 0.0000000000001136868377216160297393798828125 |
| -44 | 0.00000000000005684341886080801486968994140625 |
| -45 | 0.000000000000028421709430404007434844970703125 |
| -46 | 0.0000000000000142108547152020037174224853515625 |
| -47 | 0.00000000000000710542735760100185871124267578125 |
| -48 | 0.000000000000003552713678800500929355621337890625 |
| -49 | 0.0000000000000017763568394002504646778106689453125 |
| -50 | 0.00000000000000088817841970012523233890533447265625 |
| -51 | 0.000000000000000444089209850062616169452667236328125 |
| -52 | 0.0000000000000002220446049250313080847263336181640625 |
| -53 | 0.00000000000000011102230246251565404236316680908203125 |
| -54 | 0.000000000000000055511151231257827021181583404541015625 |
| -55 | 0.0000000000000000277555756156289135105907917022705078125 |
| -56 | 0.00000000000000001387778780781445675529539585113525390625 |
| -57 | 0.000000000000000006938893903907228377647697925567626953125 |
| -58 | 0.0000000000000000034694469519536141888238489627838134765625 |
| -59 | 0.00000000000000000173472347597680709441192448139190673828125 |
| -60 | 0.000000000000000000867361737988403547205962240695953369140625 |
| -61 | 0.0000000000000000004336808689942017736029811203479766845703125 |
| -62 | 0.00000000000000000021684043449710088680149056017398834228515625 |
| -63 | 0.000000000000000000108420217248550443400745280086994171142578125 |
| -64 | 0.0000000000000000000542101086242752217003726400434970855712890625 |
(Check out “Patterns in the Last Digits of the Positive Powers of Five” to learn about the pattern in the trailing digits.)
Here are the same powers of two, shown in fractions:
| n | 2n |
|---|---|
| -1 | 1/2 |
| -2 | 1/4 |
| -3 | 1/8 |
| -4 | 1/16 |
| -5 | 1/32 |
| -6 | 1/64 |
| -7 | 1/128 |
| -8 | 1/256 |
| -9 | 1/512 |
| -10 | 1/1,024 |
| -11 | 1/2,048 |
| -12 | 1/4,096 |
| -13 | 1/8,192 |
| -14 | 1/16,384 |
| -15 | 1/32,768 |
| -16 | 1/65,536 |
| -17 | 1/131,072 |
| -18 | 1/262,144 |
| -19 | 1/524,288 |
| -20 | 1/1,048,576 |
| -21 | 1/2,097,152 |
| -22 | 1/4,194,304 |
| -23 | 1/8,388,608 |
| -24 | 1/16,777,216 |
| -25 | 1/33,554,432 |
| -26 | 1/67,108,864 |
| -27 | 1/134,217,728 |
| -28 | 1/268,435,456 |
| -29 | 1/536,870,912 |
| -30 | 1/1,073,741,824 |
| -31 | 1/2,147,483,648 |
| -32 | 1/4,294,967,296 |
| -33 | 1/8,589,934,592 |
| -34 | 1/17,179,869,184 |
| -35 | 1/34,359,738,368 |
| -36 | 1/68,719,476,736 |
| -37 | 1/137,438,953,472 |
| -38 | 1/274,877,906,944 |
| -39 | 1/549,755,813,888 |
| -40 | 1/1,099,511,627,776 |
| -41 | 1/2,199,023,255,552 |
| -42 | 1/4,398,046,511,104 |
| -43 | 1/8,796,093,022,208 |
| -44 | 1/17,592,186,044,416 |
| -45 | 1/35,184,372,088,832 |
| -46 | 1/70,368,744,177,664 |
| -47 | 1/140,737,488,355,328 |
| -48 | 1/281,474,976,710,656 |
| -49 | 1/562,949,953,421,312 |
| -50 | 1/1,125,899,906,842,624 |
| -51 | 1/2,251,799,813,685,248 |
| -52 | 1/4,503,599,627,370,496 |
| -53 | 1/9,007,199,254,740,992 |
| -54 | 1/18,014,398,509,481,984 |
| -55 | 1/36,028,797,018,963,968 |
| -56 | 1/72,057,594,037,927,936 |
| -57 | 1/144,115,188,075,855,872 |
| -58 | 1/288,230,376,151,711,744 |
| -59 | 1/576,460,752,303,423,488 |
| -60 | 1/1,152,921,504,606,846,976 |
| -61 | 1/2,305,843,009,213,693,952 |
| -62 | 1/4,611,686,018,427,387,904 |
| -63 | 1/9,223,372,036,854,775,808 |
| -64 | 1/18,446,744,073,709,551,616 |
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