# Broken Calculator - simplified but not simple

- Author:
- Judah L Schwartz

- Topic:
- Arithmetic

Here is an example of how to use this applet -
- set a goal number to reach - say 2345
- disable the 2,3,4,5,6,7,8, and 9 keys
- use only the remaining 0 and 1 keys along and the addition & subtraction keys to get a result of 2345.
How many steps do you need? Can you do it with fewer steps?
What about a goal of 9999? How many steps do you need? Can you do it in fewer steps?

**This applet is a revised version of a program I wrote in the early 1980's entitled "What do you do with a Broken Calculator". The program was widely imitated - mostly by people with less flexible pedagogical views than I am comfortable with.**For some problem types as well as the underlying theory that drove the program's development read the essay on the Broken Calculator on the MathMindHabits website.**What problems could / would you put to your students using this applet?**Are all calculators broken?
any calculator (or digital computer, for that matter) is a rational number machine - it cannot
represent real but irrational numbers numerically. Thus, there is a large
collection of problems that calculators must produce INCORRECT answers to - for
example, 1 divided by 3.
In this case one might suppose that the calculator might distinguish between .333...3 as a
truncated decimal which is incorrect and .3 with a line over (or under) the 3 to indicate the repeating pattern.
That would be a correct answer, but one has to consider how it is arrived at.
[N.B. repeating decimals indicated with an underline, thus 1/6 = .1

__6__, 1/3 = .__3__, 1/7 = .__142857__etc.] Does the calculator ‘know’ that a pattern repeats - -by calculating until the pattern repeats and then assumes it will continue to do so? Or, -does the calculator ‘know’ the way we humans ‘know’? How do we humans know that 1/7 = .__142857__?