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Scientific Notation

Decimal Number

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Scientific Notation (e.g. 1.23e+5)

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Reviewed by Dr. Alex M., Ph.D.

Last updated: November 2025

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💡 Expert Tips

The "One Digit" Rule

Always make sure there is exactly ONE non-zero digit to the left of the decimal point. 12.3 × 10⁴ is incorrect. It should be 1.23 × 10⁵.

Positive vs Negative Exponents

Big numbers (like 1,000,000) have positive exponents. Tiny decimals (like 0.000001) have negative exponents. Think: "Negative exponent = Small number".

Calculator "E"

If your calculator says "2.5E-4", it means 2.5 × 10⁻⁴. Don't write "E" on your math test unless your teacher allows it!

⚠️ Common Mistakes

Moving the Wrong Way

When converting TO scientific notation: moving decimal Left increases the exponent (L for Larger). Moving Right decreases it (R for Reduce).

Forgetting the Sign

Don't confuse a negative number with a negative exponent. -5.2 × 10³ is a large negative number (-5200). 5.2 × 10⁻³ is a small positive number (0.0052).

Counting Zeros Instead of Places

The exponent tells you how many PLACES to move the decimal, not how many zeros to add. 1.5 × 10² is 150 (one zero), not 1500.

❓ Frequently Asked Questions

What is scientific notation? +

Scientific notation is a way to write very large or very small numbers. It uses the format a × 10ⁿ, where 'a' is a number between 1 and 10, and 'n' is an integer exponent.

How do I convert a decimal to scientific notation? +

Move the decimal point until you have a number between 1 and 10. Count how many places you moved. If you moved left, the exponent is positive. If you moved right, it's negative.

What does 'e' mean in scientific notation? +

The letter 'e' or 'E' stands for 'exponent'. For example, 1.23e+5 is the same as 1.23 × 10⁵. This format is commonly used in calculators and programming.

Why is scientific notation used? +

It makes it easier to read, write, and calculate with extremely large numbers (like the distance to stars) or extremely small numbers (like the size of atoms).

Is 0.5 × 10³ correct scientific notation? +

Technically, no. In proper scientific notation, the first number must be at least 1 and less than 10. So, 0.5 × 10³ should be written as 5.0 × 10².