# Difference between single and double in matlab?

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ABTJ on 23 Feb 2020
Edited: David Goodmanson on 23 Feb 2020
Althought both are different data types of MATLAB but what is difference between these two data types. Is it only that double has 64 bits and has more storage place and can store comparativeltly large value??
I was writing a code in MATLAB
clc
close all
clear all
x1=single(550000000)+single(5000000)+single(200000)+single(18300)
x2=550000000+5000000+200000+18300
CX1=class(x1)
CX2=class(x2)
Why do i get different answers for x1 and x2?? The last two lines CX1 and CX2 tell us that x1 is single while x2 is double but why we don't get equal value in both x1 and x2?

David Goodmanson on 23 Feb 2020
Edited: David Goodmanson on 23 Feb 2020
Hi ABT
the reason is that you are adding a small number (18300) to a large number (550000000 +5000000 + 200000) and 'single' does not have enough significant figures to accomplish this. Single needs some bits for an exponent and a sign, and there are not enough bits left over (23 in the ieee754 single-precision standard) to do the job. If you replace single with int32, there are enough bits and it works. Here int32 only needs one bit for the sign and the rest of them can contribute to significant figures.

ABTJ on 23 Feb 2020
how we can replace single with int32?
David Goodmanson on 23 Feb 2020
x1 = int32(55e7) etc. See 'doc numeric types', > create numeric variables