Basic Math Study Guide – White to Black Belt Mastery

by | Aug 11, 2025

Intro Quote or Motto

“Strong physics starts with strong math. Sharpen your basics like a blade before entering the fight.”

Key Concept (White Belt Level)

Basic math skills, scientific notation, and significant figures are the foundation of all physics calculations. Without them, solving problems accurately becomes impossible.

Core Principles

  1. Basic Math — operations with fractions, decimals, percentages, and exponents.
  2. Scientific Notation — express numbers as a × 10ⁿ, where 1 ≤ a < 10.
  3. Significant Figures — the digits in a number that convey its precision (use 3 significant figures unless stated otherwise).

Common Mistakes and Pitfalls

  • Misplacing the decimal when converting to or from scientific notation.
  • Adding or subtracting numbers with mismatched decimal places.
  • Ignoring significant-figure rules in multiplication and division.

Sensei’s Shortcuts

  • For a quick sig-fig count, start at the first non-zero digit and count to the end.
  • For ×/÷, the answer keeps the fewest significant figures among inputs.
  • For +/−, match decimal places, not significant figures.

Worked Example – Step by Step (White Belt)

Problem
Express 0.00452 in scientific notation with 3 significant figures.

Solution
Move the decimal after the first non-zero digit → 4.52 × 10⁻³.
Final Answer: 4.52 × 10⁻³

Practice Drill

  1. Write 3,200 in scientific notation with 2 significant figures.
  2. Compute (3.45 × 10³) × (2.1 × 10²) using correct significant figures.
  3. Add 45.6 and 7.89 with correct decimal precision.

Answers

  1. 3.2 × 10³
  2. 7.2 × 10⁵
  3. 53.5

Yellow Belt Extension – Deeper Skills

Convert between standard and scientific notation inside multi-step problems.
Example: Calculate speed = distance / time when both are given in scientific notation.

Black Belt Mastery – Exam Strategy and Challenge

Challenge
A physics experiment records a force of 3.4567 × 10² N applied over a distance of 0.004560 m. Calculate the work done with correct significant figures.

Sensei Strategy Notes

  • Multiply values directly (work = F × d).
  • Limit the result to the smallest significant-figure count among inputs.
  • Express the final answer in scientific notation.

Sensei’s Final Words

“Master the math first. Without precision in the basics, the advanced strikes will fail.”