Numerical Methods and Optimization

Chapter 2

Numbers and Errors

Numbers are usually represented by certain symbols, referred to as numerals,

according to rules describing the corresponding numeral system. For example,

the Roman numeral “X” describes the number ten, which is written as “10”

in the decimal system. Clearly, our capability to perform nontrivial numerical

operations efficiently depends on the numeral system chosen to represent the

numbers, and positional systems are commonly used for this purpose. In a

positional notation, each number is represented by a string of symbols, with

each symbol being a multiplier for some base number. In general, the base

number can be different