The lesson
This lesson teaches Scientific Notation. 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.
When you study the format, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Converting
When you study converting, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
- 1Move the decimal so one nonzero digit is in front of it.
- 2Count how many places you moved - that is the exponent.
- 3Large numbers get a positive exponent; small numbers (less than 1) get a negative exponent.
Write 0.00046 in scientific notation.
- 1Move the decimal 4 places right to get 4.6.
- 2Because the number is small, the exponent is negative: 4.6 × 10⁻⁴.
Why this matters
Scientific Notation shows up constantly in write huge and tiny numbers compactly using powers of 10. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- The format
- Converting
- Move the decimal so one nonzero digit is in front of it.
- Count how many places you moved - that is the exponent.
- Large numbers get a positive exponent; small numbers (less than 1) get a negative exponent.
Video walkthrough
Scientific Notation
Convert between standard form and scientific notation.
Watch on YouTubePractice
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 yourselfWrite 3,400,000 in scientific notation.
Step-by-step solution
- 1Move the decimal 6 places left: 3.4.
- 2The number is large, so use a positive exponent on 10.
- 33,400,000 = 3.4 × 10⁶.
Exercise 2
Try it yourselfWrite 0.00072 in scientific notation.
Step-by-step solution
- 1Move the decimal 4 places right to get 7.2.
- 2Because the original number is less than 1, use 10⁻⁴.
- 30.00072 = 7.2 × 10⁻⁴.
Exercise 3
Try it yourselfWrite 8.1 × 10⁵ in standard form.
Step-by-step solution
- 1Start with 8.1 and move the decimal 5 places right.
- 28.1 → 81,000 → 810,000.
- 3Standard form: 810,000.
Exercise 4
Try it yourselfMultiply: (2 × 10³)(4 × 10⁵). Write the answer in scientific notation.
Step-by-step solution
- 1Multiply coefficients: 2 × 4 = 8.
- 2Add exponents: 10³ · 10⁵ = 10⁸.
- 38 × 10⁸ is already in proper scientific notation.
Exercise 5
Try it yourselfA bacterium is about 2 × 10⁻⁶ meters wide. Write this width in standard decimal form.
Step-by-step solution
- 12 × 10⁻⁶ means move the decimal 6 places left from 2.
- 22 → 0.000002.
- 3The width is 0.000002 m.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Scientific Notation
Question 1 of 4
Write 52,000 in scientific notation.