Customizer sanitize_callback for input type number

Add a setting, specifying the sanitize_callback:

$wp_customize->add_setting(
    'my_input',
    array(
        'default' => '100.00',
        'sanitize_callback' => 'sanitize_float',
    )
);

Add the control:

$wp_customize->add_control(
    'my_input',
    array(
        'label' => 'Please enter a number:',
        'section' => 'my_section',
        'type' => 'number',
        'input_attrs' => array(
            'min' => '0.01', 'step' => '0.01', 'max' => '10000',
          ),
    )
);

Create a function to perform the sanitisation – filter_var should return the sanitised float or false:

function sanitize_float( $input ) {
    return filter_var($input, FILTER_SANITIZE_NUMBER_FLOAT, FILTER_FLAG_ALLOW_FRACTION);
}

This is untested, but should get you started – it could, of course, be adapted to sanitize an integer.

[Adapted from http://themefoundation.com/wordpress-theme-customizer/]