1. Types of Numbers
-
Whole Numbers: 0, 1, 2, 3, …
-
Integers: … –3, –2, –1, 0, 1, 2, …
-
Rational Numbers: Any number that can be expressed as a fraction (like $$\frac{3}{4}, 2.5, 0.12$$).
-
Irrational Numbers: Numbers that cannot be written as fractions ($$\sqrt{2}, \pi, e$$).
-
Prime Numbers: Integers greater than 1 divisible only by 1 and itself. (First primes: 2, 3, 5, 7, 11, …)
-
Even and Odd Integers: Even = multiple of 2; Odd = not divisible by 2.
-
Positive and Negative Numbers: Important for sign rules in multiplication/division.
ACT Tip: Be ready to identify whether a number is integer, prime, rational, or irrational.
2. Properties of Integers
-
Odd + Odd = Even
-
Even + Even = Even
-
Odd + Even = Odd
-
Odd × Odd = Odd
-
Odd × Even = Even
-
Even × Even = Even
Note: These patterns often appear in ACT logic-style questions.
3. Scientific Notation
-
Form: $$a \times 10^n$$, where $$1 \leq a < 10$$ and is an integer.
-
Example: 5,200 = $$5.2 \times 10^3$$
-
Example: 0.0047 = $$4.7 \times 10^{-3}$$
-
-
Rules:
-
Multiplying: Multiply coefficients, add exponents.
-
Dividing: Divide coefficients, subtract exponents.
-
Powers: Raise coefficient, multiply exponents.
-
ACT Tip: Be careful with negative exponents, they just mean decimal shift to the right.
4. Absolute Value
-
|x| = distance from 0 on the number line.
-
Always positive.
-
Example: |–7| = 7.
ACT Trick: When you see |x|, think two cases (x positive and x negative).
ACT Tip: In the Numbers section of the School of Mathematics ACT Qbank, you’ll find fundamental, intermediate, and advanced quizzes. Be sure to complete all of them and aim for at least 80% on each quiz before moving on to the next topic.