A Table of Negative Powers of Two

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