6th Grade Math Textbook, Fundamentals

4

,

:

1

RationalNumbers

Integers

WholeNumbers

Natura

lNumbers

 &KDSWHU

4-1

Rational Numbers

Objective To identify rational numbers • To identify rational numbers as terminating

or nonterminating repeating decimals • To locate rational numbers on a number line

Inez is a production manager for a coal mining company.
On Monday, she recorded that coal production increased
by half a ton. The following day, she recorded that coal
production fell three quarters of a ton. How can you use
rational numbers to represent the changes in the number
of tons of coal produced?

A is any number that

can be written in fractional form, ,

wherea andb are integers andb 0.

• To represent the increase in production,
  use a positive rational number.


• To represent the decrease in production,
  use a negative rational number.

So the rational numbers and  represent

the changes in the number of tons

of coal produced.

The set of rational numbers, Q, contains:

the set of natural numbers, N: 1, 2, 3,...

the set of whole numbers, W: 0, 1, 2, 3,...

the set of integers, I:... , 3, 2, 1, 0, 1, 2, 3,...

Integers can be written in fractional form and in

decimal form. For example, the integer 0 can be

written in fractional form as , and the integer  5

can be written as. The integer 4 can be written in

decimal form as 4.0, and the integer 78 can be

written as 78.0.

The set of rational numbers, Q, also includes proper

fractions, improper fractions, mixed numbers, terminating

decimals, repeating decimals, ratios, and percents.

• A is a decimal that has a finite number of decimal
  places—for example, 0.5. Every terminating decimal can be written
  as a fraction having a denominator that is a power of 10.


• A is a decimal in which a digit or sequence of digits
  repeats without end. To show that a digit or digits repeat in the decimal,
  use bar notation. Place a bar over the digit or digits that repeat—for
  example, 0.5656... 0.56, and 8.1090909 8.109.

repeating decimal

terminating decimal

 5

1

0

1

a

b

1

2

3

4

rational number

production rosehalf a ton

production fellthree quarters of a ton ^34

1

2