Consider the following code in Java :
String input = "33.3";
float num = Float.parseFloat(input);
System.out.printf("num: %f\n",num);
Why is the output of the code above
num: 33.299999 ?
Shouldn't it be
num: 33.300000 ?
I would really appreciate it if someone can explain this to me.
You're a victim of floating-point error. In base 2, 33.3 is technically a repeating binary(similar to a repeating decimal), as when written as m/n with m and n being integers and gcd(m,n)=1, the prime factors of n are not a subset of the prime factors of 2. This also means that it cannot be written as the sum of a finite number of terms m*(2^n) where m and n are integers.
A similar example happens with 7/6 in base 10.
_
1.16
becomes
1.16666667
which is then read literally, and is not equal to 7/6.
Don't use float if you can avoid it. The problem here is that %f is treating it as a double when it doesn't have that precision
String input = "33.3";
double num = Double.parseDouble(input);
System.out.printf("num: %f\n",num);
prints
33.300000
This occurs because 33.3f != 33.3 as float has less precision. To see the actual values you can use BigDecimal which covers the actual value precisely.
System.out.println("33.3f = " + new BigDecimal(33.3f));
System.out.println("33.3 = " + new BigDecimal(33.3));
prints
33.3f = 33.299999237060546875
33.3 = 33.2999999999999971578290569595992565155029296875
As you can see the true value represented is slightly too small in both cases. In the case of how %f it shows 6 decimal places even though float is not accurate to 8 decimal places in total. double is accurate to 15-16 decimal places and so you won't see an error unless the value is much larger. e.g. one trillion or more.
Double.toString(double) knew what they were doing ;)The problem is simply that float has finite precision.
32-bit floating point numbers contain enough precision for about 7 decimal places of accuracy. 33.29999 is 7 decimal places. Change "input" to be 3.3 -- you should see 3.300000 Change "input" to be 333.3 -- you will see something like :333.299988 Using a 64-bit floating point number will give you more precision (15-17 decimal places).
