xlf QandA series

Floating point precision, and cell formats

QUESTION

WHY DOES THE LOGICAL EXPRESSION FORMULA =0.1=(1.2-1.1) RETURN FALSE?


Answer icon Answer

1. Excel numbers and cell formats


The short answer to the question is: because of the way floating point numbers are processed by a computer, an expression like 1.2-1.1 actually returns 0.0999999999999999 - 15 digits (ignoring the leading zeros and decimal indicator), rather than the expected value of 0.1. This does not happen in every instance, as illustrated by the examples in figure 4.


Several methods are displayed to illustrate this feature of Double Precision floating point numbers.


2. Using Evaluate Formula to display the floating point precision value

fp-evaluate
Fig 2: Formulate Evaluate dialog box
[top panel] - the evaluate expression (the arithmetic expression in the brackets "()"), is shown by the underline. Press Evaluate to show the result of 1.2-1.1
[centre panel] - 1.2-1.1 returns 0.0999999999999999 - 15 digits (ignoring the leading zeros and decimal indicator). Press Evaluate to show the result of 0.1=0.0999999999999999
[bottom panel] - 0.1=0.0999999999999999 returns FALSE (Boolean)

3. Using F2 and F9 to display the floating point precision value

F9
Fig 3: Formula Edit, and F9 calculate
[top panel] - with the formula cell as the active cell, press F2 to enter Edit mode (shown), then select the arithmetic expression in the brackets ()
[bottom panel] - press F9 to display the result (return value) of the expression. Press ESC to discard the return expression in the formula, and show the return value FALSE

4. Floating point examples

Fig 4: Excel Web App #1
x1 - x2 = 0.1 with FALSE values shown by highlights. Column E: general format, and column H: scientific format