Download Numbers - The Basics

Math 10
City School
Numbers - The Basics1
Natural Numbers - the set of numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17,....., that we see and use every day. The natural numbers are often
referred to as the counting numbers and the positive integers.
Whole Numbers - the natural numbers plus the zero.
Integers - Any of the positive and negative whole numbers, ..., -3, -2, -1, 0, +1, +2,
+
3, ... The positive integers, 1, 2, 3..., are called the natural numbers or counting
numbers. The set of all integers is usually denoted by Z or Z+
Rational Numbers - any number that is either an integer "a" or is expressible as
the ratio of two integers, a/b. The numerator, "a", may be any whole number, and
the denominator, "b", may be any positive whole number greater than zero. If the
denominator happens to be unity, b = 1, the ratio is an integer. If "b" is other than
1, a/b is a fraction.
Fractional Numbers - any number expressible by the quotient of two numbers
as in a/b, "b" greater than 1, where "a" is called the numerator and "b" is called
the denominator. If "a" is smaller than "b" it is a proper fraction. If "a" is greater
than "b" it is an improper fraction which can be broken up into an integer and a
proper fraction.
Irrational Numbers - any number that cannot be expressed by an integer or the
ratio of two integers. Irrational numbers are expressible only as decimal fractions
where the digits continue forever with no repeating pattern. Some examples of
irrational numbers are
.
Real Numbers - the set of real numbers including all the rational and irrational
numbers.
Irrational numbers are numbers such as
Rational numbers include the whole numbers (0, 1, 2, 3, ...), the integers (..., - 2,
- 1, 0, 1, 2, ...), fractions, and repeating and terminating decimals.
Draw a line.
Put on it all the whole numbers 1,2,3,4,5,6,7.....etc
then put 0
then put all the negatives of the whole numbers to the left of 0
........-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0
Then put in all of the fractions .
Then put in all of the decimals [ some decimals aren't fractions ]
Now you have what is called the "real number line"
1.. http://www.mathgoodies.com/articles/numbers.html
Math 10
City School
Decimal Numbers - numbers expressed through the decimal, or base 10,
number system where each digit represents a multiple of some power of 10. The
term applies primarily to numbers that have fractional parts so indicated by a
decimal point. A number less than 1 is called a decimal fraction, e.g., .673. A
mixed decimal is one consisting of an integer and a decimal fraction, e.g.,
37.937.
.
Rational numbers can be expressed in the form of a fraction, 1/2, or as a
decimal, .50, 1/8, or as a decimal, .125.
A fraction expressed in decimal form will either terminate without a remainder
such as 3/8 = 0.375 or 7/8 = 0.875, repeat the same digit endlessly such as 1/3
= .3333333..... or 2/3 = .6666666....., repeat a series of different digits repeatedly
such as 1/27 = .037037037... or 1/7 = .142857142857...., or repeat a series of
digits after some non repeating digits such as 1/12 = .0833333.....
All prime denominators produce repeating decimals. All repeating decimals,
regardless of the period and length, are rational numbers integers.
Prime number – a number that has only two factors: 1 and itself.
Composite number – a number that has more than two factors.
The number 1 is neither prime nor composite.
1.. http://www.mathgoodies.com/articles/numbers.html