Friday, June 24, 2011
Practice for underflow and overflow in scientific notation.
Here is a link to a previous post about scientific notation, underflow and overflow.
Consider 80^80. If you enter this into your calculator, you will likely get an overflow error because the answer is more than 10^100. Here is how we can get around this, by splitting the number into two parts that are less than 10^100 and multiplying them together.
80^40 = 1.329227996 x 10^76
If we multiply 80^40 by 80^40, we will get 80^80. We need to square 1.329227996 to get the new significand, and the new exponent will be 10^(76+76) = 10^152
1.32922² = 1.766825808..., but since we only squared the number with six significant digits, we can only trust the answer to five significant digits, so our best answer is 1.7668 x 10^152.
Answers in the comments.