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RATIONAL NUMBERS -
numbers that can be expressed as a ratio of two
integers a and b and includes fractions,
repeating decimals, and terminating decimals
IRRATIONAL NUMBERS -
numbers that cannot be expressed as a ratio of two
integers a and b and can still be designated on a number
line
Betweeness
Refers to collinear pointsPoint B is between points
A and C if A, B, and C are collinear and AB + BC = AC
Example Three segment measures are given. Determine which point is between the other two.
AB = 12, BC = 47, and AC = 35
Measurement and Unit of Measure
Measurement is composed of the measure and the unit of measure
Measure tells you how many units
Unit of measure tells you what unit you are using
Coordinate PlaneGrid used to locate points
Divided by the y-axis and the x-axis into four quadrants
The intersection of the axes is the origin
An ordered pair of numbers names the coordinate of a point
X-coordinate is first in the ordered pair
Y-coordinate is second in the ordered pair
Postulate 2-4Each point in a coordinate plane corresponds to exactly one ordered pair of real numbers. Each ordered pair of real numbers corresponds to exactly one point in a coordinate plane.
Theorem 2-4
If a and b are real numbers, a vertical line contains all points (x, y) such that x = a, and a horizontal line contains all points (x, y) such that y = b.
Theorem 2-5Midpoint formula for a
lineOn a number line, the coordinate of the midpoint of a segment whose endpoints have coordinate a and b is a+b.
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