# GNED 1101 Chapter Notes - Chapter 2.1 : Roman Numerals, Natural Number, Land Rover Defender

2.1 Number Reprsentation and Calculation

The Hindu-Arabic & Early Positional Systems

• A ue is a astat idea that addesses the uestio how a

• A numeral is a symbol used to represent a number

• Different symbols can be used to represent the number

l l l l iv. 4.

Tally Roman Numeral Hindu – Arabic Numeral

• A system of numeration consists of a set of basic numerals and rules to represent

numbers

Exponential Notation

• If n is a natural number,

Bn = b • b • ………….

o Where b is the base and appears as a factor n times

o Bn is ead as the th powe of o to the th powe

o Bn is called an exponential expression

The Hindu Arabic System

• The system uses these ten symbols; 0, 1, 2, 3, 4, 5, 6,7, 8, 9

o Each symbol is called a digit

o These numerals can be written in expanded form using place values (hundreds,

thousandths, tens, ones etc)

• Example: Write each number in expanded form

o 663 = (6 x 100) + (6 x 10) + (0 x 1)

= (6 x 102) + (6 x 101) + ( 0 x 100)) *b0 can also be written as 1 in every case

o The positional values in this place system are based on the powers of ten

The Babylonian Numeration System

• This sste uses a ase of the powes of 6 (…, 63, 602, 601, 1)

• The system only uses two symbols with spaces to indicate place value

V <

One Ten

• Example:

o V < vv

= (1 x 602) + (10 x 601) + (1+1) x 1

= (1 x 3600) + (10 x 60) + (2 x 1)

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