Module 1 · Numbers and Operations
Chapter 5: Percentages
Problem-Solving & Data Analysis
8 topics
What this chapter covers
The 8 topics below make up Percentages on the Digital SAT. Click any topic to open its notes, examples and practice test.
1Percentage Concepts
2Percentage Increase
3Percentage Decrease
4Successive Percentages
5Discounts
6Markups
7Sales Tax
8Tips and Commissions
Study material & tests
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Formula Reference Sheet
This chapter
Core percentage
| Percent of a number | P% of N = (P/100) × N |
|---|---|
| What percent | part ÷ whole × 100% |
| Find the whole | whole = part ÷ (P/100) |
| Decimal of P% | P% = P/100 |
Change & money
| Percent change | (change ÷ original) × 100% |
|---|---|
| Increase by P% | × (1 + P/100) |
| Decrease by P% | × (1 − P/100) |
| Successive changes | multiply the factors |
| Final price w/ tax | price × (1 + tax%) |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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