Number and Quantity
ACT Number and Quantity is mostly about reading the form of a number correctly before you calculate.
核心知识
Track what the numbers represent: unit, scale, sign, form, and structure. Most ACT Number and Quantity questions become routine once you decide what kind of object you are working with.
深入理解
Rule: This topic mixes several ideas that look different on the page but demand the same habit: read carefully before computing. A ratio compares quantities, a rate carries units, an absolute value statement describes distance, a rational exponent encodes both a root and a power, and scientific notation highlights scale. Complex numbers, vectors, and matrices may appear less often, but when they do, the ACT usually asks for a direct operation, not a deep theory question.
A reliable approach is to ask four quick questions: What kind of quantity is this? What operation does the notation imply? What unit or scale should the answer have? Does the result make sense in context? If you stay disciplined about those checks, you avoid most of the trap answers in this topic.
知识点教程
9Work with rational and irrational numbers; compare magnitudes and order.
Compare rational and irrational numbers by using decimals or benchmarks on the same scale.
Use properties of exponents and radicals (including rational exponents).
Use exponent rules and rational exponents correctly, including roots and powers.
Use scientific notation and interpret scale (powers of ten, significant size comparisons).
Compare quantities in scientific notation by separating the coefficient from the power of 10.
Solve problems with absolute value, intervals, and inequality notation.
Translate absolute value inequalities into intervals and read the endpoint notation correctly.
Apply ratios, proportions, rates, and percent change in context.
Decide whether the situation calls for a ratio, rate, proportion, or percent change.
Perform unit conversions and dimensional analysis; track units consistently.
Set up unit conversions so unwanted units cancel and the final unit matches the question.
Work with complex numbers (basic operations, conjugates, magnitude where relevant).
Use i^2 = -1, combine real and imaginary parts, and rationalize denominators with conjugates.
Interpret and perform simple vector operations (components, magnitude, addition, scaling) when presented.
Add, subtract, and scale vectors by components, and use magnitude only when asked.
Interpret and use matrices for simple computations/models when presented.
Read matrices by row and column and perform the simple computations the ACT asks for.