TX PACT: Essential Academic Skills 700
(Subtest III: Mathematics - 703)
(2022/2023) (Passed with 100%)
Real numbers ✔✔are numbers that have a specific value. Real numbers can be rational or
irrational. Within rational numbers, there are integer, whole, and natural numbers.
Rational numbers ✔✔are numbers that can be expressed as a ratio (fraction or comparison) of
two integers, a/b where b ≠ 0 (because zero can't be the denominator of a fraction). All rational
numbers can be written exactly in both fraction and decimal forms, and can be graphed on a
number line. Note that exact is a formal term in mathematics meaning a value that has not been
rounded or approximated.
rational numbers ✔✔ex. mixed numbers - like 4½ which have both a whole number part, like the
"4," and a fractional part, like the "½"
ex. decimal numbers that end, such as 0.25
ex. decimal numbers that repeat the same pattern forever, such as 0.727272... (also written
0.\overline{72}0.72), which is 8/11 when written in fraction form
, Natural Numbers ✔✔real numbers that can be pointed to in nature - one tree, two people, three
dogs. This set is also known as the counting numbers; it starts at 1 and goes up by 1s in the same
way that children first learn to count, yielding the infinitely large set of values 1, 2, 3, 4, 5,...
Whole Numbers ✔✔the set of natural numbers and zero; it starts at 0 and goes up by 1s to create
the infinite set 0, 1, 2, 3, 4,...
Integers ✔✔positive and negative counting numbers and zero; the infinite set ...-3, -2, -1, 0, 1, 2,
3,...
Irrational Numbers ✔✔All include a symbol such as square root or pi
ex. must be written a symbol or radical.
real numbers that CANNOT be represented exactly as a ratio of two integers.
In order to be expressed exactly (without rounding), irrational numbers are often written with
symbols (like π, e, or \sqrt{2}2).
(Subtest III: Mathematics - 703)
(2022/2023) (Passed with 100%)
Real numbers ✔✔are numbers that have a specific value. Real numbers can be rational or
irrational. Within rational numbers, there are integer, whole, and natural numbers.
Rational numbers ✔✔are numbers that can be expressed as a ratio (fraction or comparison) of
two integers, a/b where b ≠ 0 (because zero can't be the denominator of a fraction). All rational
numbers can be written exactly in both fraction and decimal forms, and can be graphed on a
number line. Note that exact is a formal term in mathematics meaning a value that has not been
rounded or approximated.
rational numbers ✔✔ex. mixed numbers - like 4½ which have both a whole number part, like the
"4," and a fractional part, like the "½"
ex. decimal numbers that end, such as 0.25
ex. decimal numbers that repeat the same pattern forever, such as 0.727272... (also written
0.\overline{72}0.72), which is 8/11 when written in fraction form
, Natural Numbers ✔✔real numbers that can be pointed to in nature - one tree, two people, three
dogs. This set is also known as the counting numbers; it starts at 1 and goes up by 1s in the same
way that children first learn to count, yielding the infinitely large set of values 1, 2, 3, 4, 5,...
Whole Numbers ✔✔the set of natural numbers and zero; it starts at 0 and goes up by 1s to create
the infinite set 0, 1, 2, 3, 4,...
Integers ✔✔positive and negative counting numbers and zero; the infinite set ...-3, -2, -1, 0, 1, 2,
3,...
Irrational Numbers ✔✔All include a symbol such as square root or pi
ex. must be written a symbol or radical.
real numbers that CANNOT be represented exactly as a ratio of two integers.
In order to be expressed exactly (without rounding), irrational numbers are often written with
symbols (like π, e, or \sqrt{2}2).
