➕ Algebra 1 · Exponents and Polynomials
Scientific Notation cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The form
- a × 10n with 1 ≤ a < 10 and n an integer
- Positive numbers: 10 or more has a positive exponent; between 0 and 1 has a negative exponent.
- From 1 up to (but not including) 10: exponent 0
Converting
- Slide the point until one nonzero digit is on its left
- Count the slides, not the zeros
- Back to ordinary form: positive exponent slides right, negative slides left
Operations
- Multiply: fronts times fronts, exponents add
- Divide: fronts divided, exponents subtract
- Add or subtract: match the powers first, keep the power
- Then fix the front number
- Compare: the bigger exponent wins, then the front numbers (positive numbers in scientific notation)
Real sizes (all about)
- Speed of light: about 3.0 × 108 meters per second
- Sun to Earth: about 1.5 × 108 kilometers
- Human hair width: about 1 × 10−4 meters
- Kilo is 103 and milli is 10−3
Traps
- 45 × 103 is not in scientific notation
- 3.2E5 on a calculator means 3.2 × 105
- Do not add exponents when adding
Formulas
- Scientific notation: a × 10n with 1 ≤ a < 10 and n an integer
- Multiply: (a × 10m)(b × 10n) = (a × b) × 10m+n
- Divide: (a × 10m) ÷ (b × 10n) = (a ÷ b) × 10m−n
- Add: a × 10n + b × 10n = (a + b) × 10n (same exponent)
- Subtract: a × 10n − b × 10n = (a − b) × 10n (same exponent)
- How many times as large: (larger number) ÷ (smaller number)
Scientific Notation cheat sheet from HighSchoolQ.com, for personal study use.