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=== Magnitude ===
Since ''F<sub>n</sub>'' is [[Asymptotic analysis|asymptotic]] to <math>\varphi^n/\sqrt5</math>, the number of digits in {{math|''F''<sub>''n''</sub>}} is asymptotic to <math>n\log_{10}\varphi\approx 0.2090\, n</math>. As a consequence, for every integer {{math|''d'' > 1}} there are either 4 or 5 Fibonacci numbers with {{mvar|d}} decimal digits.
Fibonacci sequence of first 0 to 28 whose exponents are Fibonacci sequence:
{| class="wikitable" style="text-align:right"
! n !! F<sub>n</sub> !! F<sub>F<sub>n</sub></sub> {{OEIS|A007570}} !! Digits
|-
| 0 || 0 || 0 || 1
|-
| 1 || 1 || 1 || 1
|-
| 2 || 1 || 1 || 1
|-
| 3 || 2 || 1 || 1
|-
| 4 || 3 || 2 || 1
|-
| 5 || 5 || 5 || 1
|-
| 6 || 8 || 21 || 2
|-
| 7 || 13 || 233 || 3
|-
| 8 || 21 || 10,946 || 5
|-
| 9 || 34 || 5,702,887 || 7
|-
| 10 || 55 || 139,583,862,445 || 12
|-
| 11 || 89 || 1,779,979,416,004,714,189 || 19
|-
| 12 || 144 || 555,565,404,224,292,694,404,015,791,808 || 30
|-
| 13 || 233 || 2,211,236,406,303,914,545,699,412,969,744,873,993,387,956,988,653 || 49
|-
| 14 || 377 || 2,746,979,206,949,941,983,182,30...,998,135,811,615,145,905,740,557 || 79
|-
| 15 || 610 || 13,582,369,791,278,266,616,906,2...,870,247,715,060,398,192,490,855 || 128
|-
| 16 || 987 || 83,428,786,095,010,233,039,452,8...,203,909,274,364,258,193,729,858 || 206
|-
| 17 || 1,597 || 2,533,824,184,645,097,323,735,32...,932,445,129,029,157,243,251,977 || 334
|-
| 18 || 2,584 || 472,691,076,546,530,031,780,685,...,076,177,725,139,767,446,193,963 || 540
|-
| 19 || 4,181 || 2,678,174,576,245,943,735,375,49...,196,409,694,930,324,829,641,381 || 874
|-
| 20 || 6,765 || 2,830,748,520,089,123,910,580,48...,613,343,312,104,170,163,349,890 || 1,414
|-
| 21 || 10,946 || 16,952,165,127,657,070,069,126,3...,862,097,770,881,297,257,812,353 || 2,288
|-
| 22 || 17,711 || 107,302,901,410,621,848,261,304,...,866,972,919,879,335,166,641,889 || 3,702
|-
| 23 || 28,657 || 4,067,444,553,773,051,400,817,55...,514,294,119,121,744,055,455,137 || 5,989
|-
| 24 || 46,368 || 975,928,742,637,524,667,034,181,...,031,729,656,663,323,972,447,616 || 9,690
|-
| 25 || 75,025 || 8,876,152,444,949,440,226,201,15...,931,920,374,703,557,334,525,025 || 15,679
|-
| 26 || 121,393 || 19,369,921,626,318,966,187,122,8...,653,571,176,771,808,239,962,913 || 25,370
|-
| 27 || 196,418 || 384,448,010,820,695,855,556,132,...,820,927,828,000,174,246,945,409 || 41,049
|-
| 28 || 317,811 || 16,651,389,657,924,218,778,521,4...,467,273,617,280,084,005,430,914 || 66,419
|}
More generally, in the [[radix|base]] {{mvar|b}} representation, the number of digits in {{math|''F''<sub>''n''</sub>}} is asymptotic to <math>n\log_b\varphi = \frac{n \log \varphi}{\log b}.</math>
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