TX PACT: Essential Academic Skills 700 (Subtest III:
Mathematics - 703) 2025/2026 – Verified
Questions and Correct Answers
Real numbers - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER positive and negative counting numbers and zero; the infinite set ...-3, -2, -1,
0, 1, 2, 3,...
Irrational Numbers - ANSWER 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).
When irrational numbers are written using only ordinary numerals, they must be rounded.
Irrational numbers, by definition, cannot be written in fraction form, and when expressed as
decimals, they have infinitely many, non-repeating digits.
Irrational numbers can be approximated (π \approx 3.14≈3.14 \approx≈ 22/7; e \approx
2.72≈2.72, and \sqrt{2} \approx 1.412≈1.41) and then positioned on a number line.
Real numbers - ANSWER can be represented in a variety of ways, with the most common being
fractions, percents, and decimals.
Fractions - ANSWER usually represent partial numbers but can represent whole numbers.
½ means one half of one unit
4/1 means 4 of one unit
Mathematics - 703) 2025/2026 – Verified
Questions and Correct Answers
Real numbers - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER positive and negative counting numbers and zero; the infinite set ...-3, -2, -1,
0, 1, 2, 3,...
Irrational Numbers - ANSWER 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).
When irrational numbers are written using only ordinary numerals, they must be rounded.
Irrational numbers, by definition, cannot be written in fraction form, and when expressed as
decimals, they have infinitely many, non-repeating digits.
Irrational numbers can be approximated (π \approx 3.14≈3.14 \approx≈ 22/7; e \approx
2.72≈2.72, and \sqrt{2} \approx 1.412≈1.41) and then positioned on a number line.
Real numbers - ANSWER can be represented in a variety of ways, with the most common being
fractions, percents, and decimals.
Fractions - ANSWER usually represent partial numbers but can represent whole numbers.
½ means one half of one unit
4/1 means 4 of one unit
