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In the format commonly used for float, the closest representable value to 1,234,567.89 is 1,234,567.875.

The IEEE-754 binary32 format, also called "single precision," is commonly used for the float type. In this format, numbers are represented as ±f•2^e, where f is an integer, 0 ≤ f < 2²⁴, and e is an integer, −149 ≤ e ≤ 104. (This is expressible using different scalings for f so that it is not an integer and the range for e is adjusted accordingly so the forms are mathematically equivalent.)

Numbers in this form are encoded using 32 bits:

• The + or − is encoded in one bit.
• Of the 24 binary digits of f, 23 are encoded explicitly in 23 bits.
• The exponent range, −149 ≤ e ≤ 104, spans 254 numbers, so this is encoded in 8 bits. 8 bits can encode 256 numbers, so the other two values are used to represent infinities, NaNs ("Not a Number"), and cases where the leading bit of f is zero.

In this format, the closest representable number to 1,234,567.89 is +9,876,543•2⁻³ = 1,234,567.875. Since f must be an integer, the next greater representable number is +9876544•2⁻³ = 1,234,568. (We cannot make the number any finer by using 2⁻⁴ instead of 2⁻³ because then f would have to change to about double of 9,876,543, and that would make it larger than 2²⁴.)

So, when atof("1234567.89") returns 1,234,567.875, it is returning the best possible result.