Unit 1 · Topic 2

Scientific Notation

Overview

Write huge and tiny numbers compactly using powers of 10.

Topic 2 of 3~22 min
Next: Roots & Irrational NumbersAll units
Unit overview

The lesson

Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

The format

Scientific notation writes a number as (a value from 1 up to 10) × 10 raised to a power. Example: 125,000,000 = 1.25 × 10⁸.

Converting

  1. 1Move the decimal so one nonzero digit is in front of it.
  2. 2Count how many places you moved - that is the exponent.
  3. 3Large numbers get a positive exponent; small numbers (less than 1) get a negative exponent.
Worked example

Write 0.00046 in scientific notation.

  1. 1Move the decimal 4 places right to get 4.6.
  2. 2Because the number is small, the exponent is negative: 4.6 × 10⁻⁴.

Why this matters

Write huge and tiny numbers compactly using powers of 10.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.

Re-reading the question too quickly. Underline what you are solving for before you start calculating.

Key ideas from this lesson

  1. The format
  2. Converting
  3. Move the decimal so one nonzero digit is in front of it.
  4. Count how many places you moved - that is the exponent.
  5. Large numbers get a positive exponent; small numbers (less than 1) get a negative exponent.

Video walkthroughs

Math Antics

Scientific Notation

Convert between standard form and scientific notation.

Watch on YouTube
Khan Academy

Scientific Notation Examples

Convert between standard form and scientific notation.

Watch on YouTube
Khan Academy

Subtracting in Scientific Notation

Add and subtract numbers written in scientific notation.

Watch on YouTube
Khan Academy

Multiplying and Dividing in Scientific Notation

Operate on numbers in scientific notation efficiently.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

Write 3,400,000 in scientific notation.

Step-by-step solution

  1. 1Move the decimal 6 places left: 3.4.
  2. 2The number is large, so use a positive exponent on 10.
  3. 33,400,000 = 3.4 × 10⁶.

Exercise 2

Try it yourself

Write 0.00072 in scientific notation.

Step-by-step solution

  1. 1Move the decimal 4 places right to get 7.2.
  2. 2Because the original number is less than 1, use 10⁻⁴.
  3. 30.00072 = 7.2 × 10⁻⁴.

Exercise 3

Try it yourself

Write 8.1 × 10⁵ in standard form.

Step-by-step solution

  1. 1Start with 8.1 and move the decimal 5 places right.
  2. 28.1 → 81,000 → 810,000.
  3. 3Standard form: 810,000.

Exercise 4

Try it yourself

Multiply: (2 × 10³)(4 × 10⁵). Write the answer in scientific notation.

Step-by-step solution

  1. 1Multiply coefficients: 2 × 4 = 8.
  2. 2Add exponents: 10³ · 10⁵ = 10⁸.
  3. 38 × 10⁸ is already in proper scientific notation.

Exercise 5

Try it yourself

A bacterium is about 2 × 10⁻⁶ meters wide. Write this width in standard decimal form.

Step-by-step solution

  1. 12 × 10⁻⁶ means move the decimal 6 places left from 2.
  2. 22 → 0.000002.
  3. 3The width is 0.000002 m.

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Khan Academy

Scientific notation

Open resource
Math Worksheets 4 Kids

Scientific notation worksheets

Open resource

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Scientific Notation

Question 1 of 4

Easy

Write 52,000 in scientific notation.

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