why does the number 51444.325061 doesnot round off to 51444.325 upto 3 decimal places? I want to round off this number in c programming

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#include <stdio.h>
#include <stdlib.h>

int main() {
    float n;
    scanf("%f", &n);
    printf("%.3f", n);
}

input: 51444.325061

my output: 51444.324

expected output: 51444.325

why does I dont get the proper answer?

precision decimal floating-point rounding c
2 Answers

32-bit float can encode about 232 different values.

51444.325061is not one of them**. Instead the nearest float is exactly 51444.32421875. The next best choice would be 51444.328125.

Printing 51444.32421875 to 3 decimal places is best as "51444.324".

why does I dont get the proper answer?

float is too imprecise to encode 51444.325061 as OP desires. Using double will help. The same problem exists, yet only appears when about 16+ significant digits are needed.

** Encodable finite values are of the form: some_integer * 2some_exponent.

user_24103590

Internally, floating-point numbers are not represented as decimal fractions, as you might expect. Instead, they use a floating-point representation based on binary (base-2) numbers.

Because they're base-2, these floating-point numbers cannot represent decimal fractions exactly.

Here are the available float values nearest to 51444.325061, along with their exact decimal equivalents:

0x4748f452  51444.32031250  0.784978032112121582031250 × 2^16
0x4748f453  51444.32421875  0.784978091716766357421875 × 2^16
0x4748f454  51444.32812500  0.784978151321411132812500 × 2^16
0x4748f455  51444.33203125  0.784978210926055908203125 × 2^16

So you can take your pick between 51444.324 or 51444.328. But obviously 51444.324 is closer.

user_39238960
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