Applied Math: Numbers

Classifications of Numbers
 

Numbers are the basic building blocks of mathematics. Specific features of numbers are identified by the following terms:
Integer – any positive or negative whole number, including zero. Integers do not include fractions , decimals (0.56), or mixed numbers .
Prime number – any whole number greater than 1 that has only two factors, itself and 1; that is, a number that can be divided evenly only by 1 and itself.
Composite number – any whole number greater than 1 that has more than two different factors; in other words, any whole number that is not a prime number. For example: The composite number 8 has the factors of
1, 2, 4, and 8.
Even number – any integer that can be divided by 2 without leaving a remainder. For example: 2, 4, 6, 8, and so on.
Odd number – any integer that cannot be divided evenly by 2. For example: 3, 5, 7, 9, and so on.
Decimal number – any number that uses a decimal point to show the part of the number that is less than one. Example: 1.234.
Decimal point – a symbol used to separate the ones place from the tenths place in decimals or dollars from cents in currency.
Decimal place – the position of a number to the right of the decimal point. In the decimal 0.123, the 1 is in the first place to the right of the decimal point, indicating tenths; the 2 is in the second place, indicating hundredths; and the 3 is in the third place, indicating thousandths.
The decimal, or base 10, system is a number system that uses ten different digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). An example of a number system that uses something other than ten digits is the binary, or base 2, number system, used by computers, which uses only the numbers 0 and

1. It is thought that the decimal system originated because people had only their 10 fingers for counting.
Rational numbers include all integers, decimals, and fractions. Any terminating or repeating decimal number is a rational number.
Irrational numbers cannot be written as fractions or decimals because the number of decimal places is infinite and there is no recurring pattern of digits within the number. For example, pi (π) begins with

3.141592 and continues without terminating or repeating, so pi is an irrational number.
Real numbers are the set of all rational and irrational numbers.


The Number Line
A number line is a graph to see the distance between numbers. Basically, this graph shows the relationship between numbers. So a number line may have a point for zero and may show negative numbers on the left side of the line. Also, any positive numbers are placed on the right side of the line. For example, consider the points labeled on the following number line:

We can use the dashed lines on the number line to identify each point. Each dashed line between two whole numbers is .

The line halfway between two numbers is .

Numbers in Word Form and Place Value
When writing numbers out in word form or translating word form to numbers, it is essential to understand how a place value system works. In the decimal or base-10 system, each digit of a number represents how many of the corresponding place value – a specific factor of 10 – are contained in the number being represented. To make reading numbers easier, every three digits to the left of the decimal place is preceded by a comma.

The following table demonstrates some of the place values:

Power of 10
Value	1,000	100	10	1	0.1	0.01	0.001
Place	thousands	hundreds	tens	ones	tenths	hundredths	thousandths

 
For example, consider the number 4,546.09, which can be separated into each place value like this:

 
This number in word form would be four thousand five hundred forty-six and nine hundredths.

Absolute Value
A precursor to working with negative numbers is understanding what absolute values are.

A number’s absolute value is simply the distance away from zero a number is on the number line.

The absolute value of a number is always positive and is written . For example, the absolute value of 3, written as , is 3 because the distance between 0 and 3 on a number line is three units. Likewise, the absolute value of –3, written as  is 3 because the distance between 0 and –3 on a number line is three units. So .


Practice
P1. Write the place value of each digit in 14,059.826
P2. Write out each of the following in words:
(a) 29
(b) 478
(c) 98,542
(d) 0.06
(e) 13.113
 

P3. Write each of the following in numbers:
(a) nine thousand four hundred thirty-five
(b) three hundred two thousand eight hundred seventy-six
(c) nine hundred one thousandths
(d) nineteen thousandths
(e) seven thousand one hundred forty-two and eighty-five hundredths

Practice Solutions
P1. The place value for each digit would be as follows:

P2. Each written out in words would be: (a) twenty-nine
(b) four hundred seventy-eight
(c) ninety-eight thousand five hundred forty-two
(d) six hundredths
(e) thirteen and one hundred thirteen thousandths P3. Each in numeric form would be: (a) 9,435
(b) 302, 876
(c) 0.901
(d) 0.019
(e) 7,142.85