Scientific Notation Calculator & Converter
Convert any number to scientific notation, convert scientific notation back to standard form, perform operations, and get step-by-step explanations — instantly.
Multiply, divide, add or subtract two numbers in scientific notation with full step-by-step working.
Scientific Notation Calculator — Complete Guide
This scientific notation calculator and converter handles everything: converting decimal numbers to scientific notation, converting scientific notation back to standard form, and performing all four arithmetic operations with full step-by-step working. Whether you're a student, scientist, or engineer, this tool makes working with very large and very small numbers effortless.
How to Use the Scientific Notation Converter
- Choose your conversion direction using the two mode buttons at the top of the calculator.
- Decimal → Scientific Notation: Enter any number (like
673.5or0.000006) and click Convert. - Scientific Notation → Standard Form: Enter the coefficient (e.g.
6.735) and the exponent (e.g.2) and click Convert. - Use the Operations section to multiply, divide, add, or subtract two numbers already in scientific notation.
- Click the example chips to load famous numbers instantly.
- Download a free printable worksheet below for practice problems.
What Is Scientific Notation?
Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in decimal form. A number in scientific notation is written as:
a × 10ⁿ — where 1 ≤ |a| < 10 (the coefficient) and n is any integer (the exponent).
For example, the speed of light is 299,792,458 m/s — in scientific notation this is 2.998 × 10⁸. Much cleaner, and the exponent instantly tells you the magnitude of the number.
673.5 in Scientific Notation — Step-by-Step
One of the most searched examples: write the number 673.5 in scientific notation. Here's exactly how to do it:
- Start with
673.5. We need the coefficient to be between 1 and 10. - Move the decimal point 2 places to the left:
673.5 → 6.735 - Because we moved the decimal 2 places left, the exponent is +2.
- Write as:
6.735 × 10² - Verification:
6.735 × 100 = 673.5✓
Click the "673.5" chip in the calculator above to see full working automatically!
Scientific Notation Rules
To correctly write any number in scientific notation, follow these rules:
- Rule 1 — The coefficient must be ≥ 1 and < 10. So 6.735 is valid; 67.35 is not.
- Rule 2 — The base is always 10. You always write × 10ⁿ.
- Rule 3 — Large numbers have positive exponents. Moving the decimal left → positive n. E.g. 5000 = 5 × 10³.
- Rule 4 — Small numbers (less than 1) have negative exponents. Moving the decimal right → negative n. E.g. 0.005 = 5 × 10⁻³.
- Rule 5 — Count the decimal moves carefully. The number of places you move the decimal IS the exponent.
- Rule 6 — The sign of the exponent shows direction, not size. 10⁻³ means tiny (thousandths); 10³ means large (thousands).
How to Convert a Number to Scientific Notation
Use this step-by-step method every time:
- Identify the original decimal point position (or assume it's at the far right for whole numbers).
- Move the decimal point until the number is between 1 and 10. That number is your coefficient a.
- Count how many places you moved. That count is the absolute value of your exponent.
- If you moved the decimal left, the exponent is positive.
- If you moved the decimal right, the exponent is negative.
- Write the result as a × 10ⁿ.
Example: 0.006 in Scientific Notation
- Start:
0.006 - Move decimal 3 places right to get
6.0 - Moved right → exponent is negative 3
- Result:
6.0 × 10⁻³ - Check:
6.0 ÷ 1000 = 0.006✓
Example: Speed of Light in Scientific Notation
- Speed of light =
299,792,458m/s - Move decimal 8 places left:
2.99792458 - Moved left → exponent is +8
- Rounded to 4 sig figs:
2.998 × 10⁸
Example: 1 Billion in Scientific Notation
- 1 billion =
1,000,000,000 - Move decimal 9 places left:
1.0 - Result:
1.0 × 10⁹
How to Convert Scientific Notation to Standard Form
To go from scientific notation back to a regular decimal number (standard form):
- Look at the exponent n.
- If n is positive, move the decimal point n places to the right. Add zeros if needed.
- If n is negative, move the decimal point |n| places to the left. Add leading zeros if needed.
Example: 6.735 × 10² to Standard Form
- Exponent is +2 → move decimal 2 places right.
6.735 → 673.5
How to Multiply in Scientific Notation
Multiplying two numbers in scientific notation is straightforward:
(a × 10ⁿ) × (b × 10ᵐ) = (a × b) × 10^(n+m)
Step 1: Multiply the coefficients. Step 2: Add the exponents. Step 3: Adjust if the new coefficient is not between 1 and 10.
Example: (3.0 × 10⁴) × (2.0 × 10³)
- Multiply coefficients:
3.0 × 2.0 = 6.0 - Add exponents:
4 + 3 = 7 - Result:
6.0 × 10⁷
How to Divide in Scientific Notation
(a × 10ⁿ) ÷ (b × 10ᵐ) = (a ÷ b) × 10^(n−m)
Example: (8.0 × 10⁶) ÷ (2.0 × 10²)
- Divide coefficients:
8.0 ÷ 2.0 = 4.0 - Subtract exponents:
6 − 2 = 4 - Result:
4.0 × 10⁴
How to Add and Subtract in Scientific Notation
Addition and subtraction require matching exponents first:
- Make both exponents the same (convert the smaller-exponent number).
- Add or subtract the coefficients.
- Keep the common exponent.
- Adjust to proper scientific notation if needed.
Example: (3.0 × 10⁴) + (2.0 × 10³)
- Convert second number:
2.0 × 10³ = 0.2 × 10⁴ - Add:
(3.0 + 0.2) × 10⁴ = 3.2 × 10⁴
Scientific Notation Operations — Quick Reference
| Operation | Rule | Example | Answer |
|---|---|---|---|
| × | Multiply coefficients, add exponents | (2 × 10³)(3 × 10²) | 6 × 10⁵ |
| ÷ | Divide coefficients, subtract exponents | (6 × 10⁵) ÷ (3 × 10²) | 2 × 10³ |
| + | Match exponents, then add coefficients | (3 × 10⁴)+(2 × 10⁴) | 5 × 10⁴ |
| − | Match exponents, then subtract coefficients | (5 × 10³)−(2 × 10³) | 3 × 10³ |
Free Scientific Notation Worksheet — Printable Practice Problems
Practice makes perfect. Use these problems to test your understanding of scientific notation. Click the download button to get a formatted printable PDF version.
Scientific Notation Practice Worksheet
Convert each number to scientific notation. Write your answers in the space provided.
Includes answer key • Printable A4 & Letter size • Free forever
Frequently Asked Questions
6.735 × 10² → move decimal 2 right → 673.5. And 6.0 × 10⁻³ → move decimal 3 left → 0.006.(3.0 × 10⁴) + (2.0 × 10³) → convert: (3.0 × 10⁴) + (0.2 × 10⁴) → 3.2 × 10⁴. Use the Operations section above!| Number | Sci. Notation |
|---|---|
| 673.5 | 6.735 × 10² |
| 0.006 | 6.0 × 10⁻³ |
| 1 billion | 1.0 × 10⁹ |
| Speed of light | 2.998 × 10⁸ |
| Avogadro's No. | 6.022 × 10²³ |
| Electron mass | 9.109 × 10⁻³¹ |
| Planck const. | 6.626 × 10⁻³⁴ |
| Earth's mass | 5.972 × 10²⁴ |
| Standard | Sci. Notation |
|---|---|
| 0.001 | 1 × 10⁻³ |
| 0.01 | 1 × 10⁻² |
| 0.1 | 1 × 10⁻¹ |
| 1 | 1 × 10⁰ |
| 10 | 1 × 10¹ |
| 100 | 1 × 10² |
| 1,000 | 1 × 10³ |
| 1,000,000 | 1 × 10⁶ |