Notes for Homework 1

Notes on rounding and rounding error with fractions.


Notes on binary and decimal representation of numbers.


Notes on rounding to significant digits. 


The link to rounding to significant digits deals with rounding a number great than 1. For example 2^16 = 65,536.

65,536 rounded to one significant digit = 70,000

65,536 rounded to two significant digits = 66,000
65,536 rounded to three significant digits = 65,500

Let's consider rounding a number less than 1.

2^(-16) = 0.000015258789...

If we were asked to round this to the nearest thousandth, we would get 0.000. It's never a good idea to round a number that isn't zero to zero. Doing this means we aren't thinking at the right scale. Rounding to significant digits ensures we will never round a non-zero number to zero.

0.000015258789... rounded to one significant digit = 0.00002
0.000015258789... rounded to two significant digits = 0.000015
0.000015258789... rounded to three significant digits = 0.0000153

In most cases except scientific papers, rounding to three significant digits is considered sufficient.

Practice problems for the test on 7/2

The Transformers sequel made $108,966,307 this weekend.

a) Round this number to one significant digit.
b) Round this number to two significant digits.
c) Round this number to three significant digits.

According to the calculator 50! rounds to 3.041 x 10^64 and 60! rounds to 8.321 x 10^81, both rounded to four significant digits. Find the following values.

d) 50! / 60!
e) 60! / 50!
f) 50! x 60!
(note: the calculator will tell you overflow error on problem f because it doesn't like numbers bigger than 10^100 power. You will have to do this one by hand.)

Answers in the comments.