Random digits printed when printing more than 6 decimal digits in float datatype in C (GCC compiler)

Question

I was executing following C code-

float a=3.25678932;
printf("%0.10f\n",a);

The above printf() statement giving following output:

3.2567892075

I am not able to understand how other four digits('2075') are coming after first six digits('256789') after decimal.

That sounds perfectly normal. Do you know how floating point numbers work in computers? — Shawn, Mar 01 '20 at 16:57
https://stackoverflow.com/questions/5098558/float-vs-double-precision — Mat, Mar 01 '20 at 16:59

score 2 · Accepted Answer · answered Mar 01 '20 at 17:23

Your C implementation likely uses the IEEE-754 binary32 format for float. In this format, every finite number is, in effect, a sign (+ or −) applied to a 24-bit integer M multiplied by some power of two.

Since 2¹ ≤ 3.25678932 < 2², the power of two used is 2²⁻²⁴ = 2⁻²². (The −24 scales the 24-bit integer to between ½ and 1, and the 2 scales that to between 2 and 4.)

Then, to choose the integer M, we choose the integer that is closest to 3.25678932/2⁻²². 3.25678932/2⁻²² is about 13,659,964.472, so we use 13,659,964.

Thus, the result of converting 3.25678932 to float is 13,659,964•2⁻²², which is exactly 3.25678920745849609375.

When you print this rounded to 10 digits after the decimal point, the result is “3.2567892075”.

Random digits printed when printing more than 6 decimal digits in float datatype in C (GCC compiler)

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