I want to know the difference between 1 and 1.0000

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When I do logarithms, I run into some difficulties.
d3=697.5512; f1=697.5512;
And the result is a=1.0000; and log10(a)=-9.643274665532978e-15
But if I type d=1.0000,the result is d=1; log10(d)=1

Accepted Answer

Abolfazl Chaman Motlagh
Abolfazl Chaman Motlagh on 7 Sep 2021
Edited: Abolfazl Chaman Motlagh on 7 Sep 2021
first of all log10(1) should be zero!
but beside this,
i think you are reporting your workspace wich is produced after some calculation. and you thought the number you see is exactly what it is. the d3 and f1 might not be exactly what you see in workspace , it just show 4 decimal digits of them.
i am copying your code and run it here to see what i mean :
ans = 0
you see it is correct but here i am resolving your result to see what i meant before :
format long
d3_ = f1 * (10^(-9.643274665532978e-15))
d3_ =
so d3 and f1 are not exactly what is reported in user interface of workspace. for see them more precisely call
format long
and print them. (or use vpa function)

More Answers (1)

Jan on 7 Sep 2021
Edited: Jan on 7 Sep 2021
The output is mimited to 4 digits after the decimal point. Then "1" means 1.0, and "1.0000" means that there is a digit differing from 0 hidden on the right.
Check this by:
a - 1 % Not 0
d - 1 % 0
e1 - 1 % Not 0

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