Questions about the accuracy and scope of float and int in Java

I have discussed with my classmates, the transformation between float and int in Java, before the one-sided learning of the Java Foundation, the sense of the int type is not as high as the float type, because float can represent decimals, and int can only represent integers.

It turned out to be not the case (Java Core Programming volume P (43)): Example 123456789 is a larger int-type integer that has the same result size when it goes float. However, because the number of digits represented by INT (32-bit) is more than the number of digits represented by float (32-1 (sign bit)-8 (digit) = 23-bit), so the int is more accurate than float, and may lose precision when int is float, and float has 8-bit exponential bit, Therefore, the value of float storage is greater than int.