How to check the accuracy of estimation

Using the approximated volume i have 0.51666667 and the true volume is 0.52359878 , the error is 0. 00 693211 so it will be accurate by 2 decimal places. How do i only print the values if only the decimal place has increased by 1? I used floor(-log10(error)) but it counted incorrectly as the error gets smaller. For points of 168, the zeros in front should be 5, but it calculated to be 6 . May i know what is wrong?

[Stephen23]

"For points of 168, the zeros in front should be 5, but it calculated to be 6 . May i know what is wrong?"

Look more closely at the error value and you will find that it actually has 6 leading zeros. Try fprintf to thirty significant figures, or download and use James Tursa's excellent num2strexact.

Welcome to the world of floating point numbers! Note that how floating point numbers are displayed is not the same thing as what value is actually stored in memory.

Answer 1

[Walter Roberson]

Observe:

>> fprintf('%.8f\n', 0.000000999)
0.00000100

Actual number of leading 0: 6. The 5 visible are due to rounding for presentation.