Chapter 1 Integers and Rational Numbers

terminating decimal

A decimal number that has digits that do not go on forever. Examples: 0.25 (it has two decimal digits) 0.123456789 (it has nine decimal digits) In contrast a Recurring Decimal has digits that go on forever Example of a Recurring Decimal: 1/3 = 0.333... (the 3 repeats forever)

repeating decimal

A decimal number that has digits that repeat forever. Examples: 1/3 = 0.333... (the 3 repeats forever) 1/7 = 0.14285714285... ( the "142857" repeats forever) 77/600 = 0.128333... (the 3 repeats forever) The part that repeats is usually shown by placing dots over the first and last digits of the repeating pattern, or sometimes a line over the pattern.

integers

A number with no fractional part. Includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...} You can write them down like this: {..., -3, -2, -1, 0, 1, 2, 3, ...} Examples of integers: -16, -3, 0, 1, 198

reciprocals

Reciprocal To get the reciprocal of a number, just divide 1 by the number Example: the reciprocal of 2 is 1/2 (half) Every number has a reciprocal except 0 (1/0 is undefined) The reciprocal is shown as 1/x, or x-1 If you multiply a number by its reciprocal you get 1 Example: 3 times 1/3 equals 1

opposites

The opposite of a number is just the number on the opposite side of zero on the number line. The opposite of a is -a. The opposite of -a is a.

additive inverse

What you add to a number to get zero. The negative of a number. Example: The additive inverse of -5 is 5, because -5 + 5 = 0. The additive inverse of +5 is -5 as well.

rational number

Any number that can be made by dividing one integer by another. The word comes from "ratio". Examples: 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2) 0.75 is a rational number (3/4) 1 is a rational number (1/1) 2 is a rational number (2/1) 2.12 is a rational number (212/100) -6.6 is a rational number (-66/10) But Pi is not a rational number, it is an "Irrational Number".

absolute value

How far a number is from zero. Example "6" is 6 away from zero, but "-6" is also 6 away from zero. So, the absolute value of 6 is 6, and the absolute value of -6 is also 6. The symbol "|" is placed either side to mean "Absolute Value", so we can write: |-6| = 6