A python function to correctly print a value with its error in scientific format and the correct number of significant figures.

round_on_error.py

# Return the power of ten of a string in scientific notation
# "3.42e3" --> 3
def get_power_of_ten(scientific_notation):
    # Split the scientific notation into coefficient and exponent parts
    coefficient, exponent = scientific_notation.split('e')
    return int(exponent)

# Returns the value with significant figures up to the error position
# Example round_on_error(2.586e-1, 3.304e-2) => 2.6e-01 ± 3.3e-02
def round_on_error(val, err):
    val_power_ten = get_power_of_ten(f'{val:.10e}')
    err_power_ten = get_power_of_ten(f'{err:.10e}')
    significant_numbers = abs(err_power_ten - val_power_ten)
    significant_numbers_err = min(3,significant_numbers)

    formatted_result = "{f_val:.{SN}f}e{f_exp:+03} ± {f_err:.{SNerr}f}e{f_exp_err:+03}".format(
    f_val=val*10**(-val_power_ten), SN=significant_numbers, SNerr= significant_numbers_err,
    f_exp = val_power_ten, f_exp_err = err_power_ten, f_err=err*10**(-err_power_ten))
    
    formatted_value = "{f_val:.{SN}f}e{f_exp:+03}".format(
    f_val=val*10**(-val_power_ten), SN=significant_numbers, f_exp = val_power_ten)
    
    formatted_error = "{f_err:.{SNerr}f}e{f_exp_err:+03}".format(
    SNerr= significant_numbers_err, f_exp_err = err_power_ten, f_err=err*10**(-err_power_ten))

    return formatted_result, formatted_value, formatted_error