Chapter 1 Numbers and the Base Ten System

Decimal system

also known as the base 10 system

Counting numbers

(also known as natural numbers) any number that you can use for counting things: 1, 2, 3, 4, 5, ... (counting numbers are also cardinal)

Number path

a counting model used a precursor to the number line

Number line

a line that represents the set of all real numbers in order

Whole numbers

are made up of counting numbers (natural numbers) including zero

Scale

choice of the unit used on the number line

Unit

distance between each number on a number line

List set

group of numbers or objects that represent a range of values

Expanded form

it is shown as a sum of each digit multiplied by its matching place value (units,tens, hundreds, etc.) such as 231=(2x100)+(3x10)+(1x1)=200+30+1

One-to-one correspondence

situation in which the members of one set (call it A) can be evenly matched with the members of a second set (call it B)

Base-ten representation

string of digits that represents a number such as 1,234

Digit

ten distinct symbols used in the base-ten system, namely, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Base-ten system

the base 10 number system is known as the decimal system and has 10 digits to show all numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, using place value and decimal point to separate whole numbers from decimal fractions

Cardinality of a set

the number of "things" in a set (cardinal counting numbers telling "how many")

Place value

the numerical value that a digit has by virtue of its position in a number