What does it mean when a calculator has an overflow error?

In: Mathematics

Simplified answer: Calculators can only hold a limited number of digits. If your calculation results in a number beyond what the calculator can hold, it will result in an overflow. For example if the calculator can only hold 10 digits and you try to multiply two 6-digit numbers, the result is a 12-digit number which the calculator can’t hold.

A little more precise answer: The calculator actually holds the current number as a [floating point number](https://en.wikipedia.org/wiki/Floating-point_arithmetic). This means that the calculator stores the number as a value (called a *significand* or *mantissa*) multiplied by a power of 2 (or 10). For example, the number 4525 would actually be 4.525 × 10^(3). The significand and the exponent each have a limited number of digits, so if you pass this number, you get an overflow. For example, a TI-84 calculator can’t handle numbers larger than 9.99999999 × 10^(99), so if you tried to multiply 10^(70) with itself, you get an overflow.

It’s a bit like an [analog odometer](https://editorial.pxcrush.net/carsales/general/editorial/odometer-day-102.jpg?width=1024&height=683). Calculators and computers only have a finite amount of bytes to store numbers in. On an odometer once you hit the highest number it can display (like 9999 on a 4-digit odometer), the next number will wrap it around back to 0000.

It gets a little bit more complicated when you consider negative or floating point numbers, but the basic idea still holds.

The storage for the number is too small and it starts all over. Think of it like that way: you have a very long number on paper, and you run out of paper.