# why does realmax('single') display 8 digits?

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Sean Doherty on 17 Dec 2020
Commented: Sean Doherty on 18 Dec 2020
most texts agree that IEEE-754 sinlge persision has 7 signicant digits and double percision has 15
so why does realmax('single') display 8 digits and realmax('double') display 16 digits?
Sean Doherty on 18 Dec 2020
Thakyou Stephen. This clarifies things. I would have accepted your answer, but not offered that option

Ameer Hamza on 17 Dec 2020
Edited: Ameer Hamza on 17 Dec 2020
"most texts agree that IEEE-754 sinlge persision has 7 signicant digits and double percision has 15"
But they don't. More precisely, they have 24 and 53 significant binary digits, respectively. Both are capable of representing 2^24 and 2^53 consecutive integers without any loss of precision. MATLAB just returns these values.
Note that it is still possible to represent even bigger integers with full precision, but the only issue is that the number adjacent to them cannot be represented precisely.
Read here: https://en.wikipedia.org/wiki/IEEE_754#Basic_and_interchange_formats. They are capable of representing ~7.22 and ~15.96 decimal digits respectively.
Walter Roberson on 17 Dec 2020
Given N digits of a single precision number, is entering those N digits enough to exactly reproduce the same bit pattern?
fprintf('%1.20e\n', single(5.960464e-8))
5.96046412226769461995e-08
fprintf('%1.20e\n', single(5.9604644e-8))
5.96046447753906250000e-08
So 7 input digits is not enough to completely preproduce 2^-24 but 8 input digits is. Therefor, this particular number has 8 significant decimal digits in single precision. But there are other values that use "all" of the digits (no trailing 0 in decimal) that 7 copied digits is enough.

Walter Roberson on 17 Dec 2020
>> flintmax('single')
ans =
single
16777216
You get 7 full digits, up to 9999999 . And there is some spare room beyond that, but not enough for a full digit. It is about 7.22 digits.

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