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.
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.
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.
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