Key takeaways
- n = m × 10ᵏ, where the mantissa m is always between 1 and 10.
- Move the decimal point left for a positive exponent, right for a negative one.
- 93,000,000 becomes 9.3 × 10⁷.
- Count the places moved carefully — that count IS the exponent.
In this guide
What is scientific notation?
Instead of writing a huge number like 93,000,000 in full, scientific notation writes it as 9.3 × 10⁷ — a compact form that's easier to read, compare, and use in calculations.
Why does scientific notation matter?
Scientists, engineers, and astronomers deal with numbers spanning many sizes at once, from the width of an atom to the distance between stars. Scientific notation keeps every one of those numbers just as short and easy to compare.
93,000,000 miles becomes just 9.3 × 10⁷ — seven characters saved and instantly easier to compare with another distance written the same way.
The formula
| Symbol | What it means | Example |
|---|---|---|
| n | The original number | 93,000,000 |
| m | The mantissa: a decimal number between 1 and 10 (not including 10) | 9.3 |
| k | The exponent: how many places the decimal point moved | 7 |
How to write scientific notation step by step
- 1Find where the decimal point currently is in your number (at the end, for a whole number).
- 2Move the decimal point until only one non-zero digit remains before it, so the number becomes between 1 and 10.
- 3Count how many places you moved the decimal point — that count is your exponent, k.
- 4Write your answer as m × 10ᵏ, positive if you moved left (large numbers), negative if you moved right (small numbers).
Enter your own number in the calculator below to see the decimal-shifting steps.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Getting the sign of the exponent backwards. Moving the decimal point left (for large numbers) gives a positive exponent; moving it right (for small numbers) gives a negative exponent.
- Miscounting the decimal places. Recount carefully, especially with numbers that have many zeros.
- Forgetting the ×10 part entirely and leaving just the mantissa as the final answer.
Tips and tricks
- For small decimals, count how many places you move right past leading zeros to reach the first non-zero digit — that count becomes a negative exponent.
- Double-check by mentally multiplying the mantissa by 10ᵏ and confirming it matches your original number.
- Scientific notation is built entirely on exponents, so it's worth being comfortable with powers first.
Where you'll use it in real life
- Astronomy: writing distances between planets, stars, or galaxies compactly.
- Science: recording microscopic measurements, like the size of a cell or a virus.
- Finance: expressing very large figures, like national budgets, in a readable form.
- Computing: representing extremely large or small values in calculations and displays.
Quick summary
To write a number in scientific notation, move its decimal point until only one non-zero digit remains before it, then record how many places you moved as the exponent. Moving left gives a positive exponent, moving right gives a negative one. Try the calculator above with your own number.
Worked example
The average distance from Earth to the Sun is about 93,000,000 miles. How would you write that distance in scientific notation?
- 01n = m × 10^k where 1 ≤ |m| < 10
- 02Move the decimal point 7 place(s) left
- 0393000000 = 9.3 × 10^7
- 04Mantissa = 9.3, Exponent = 7
These numbers are pre-filled in the calculator above.
Frequently asked questions
Why is scientific notation useful?
It makes extremely large or small numbers much shorter to write and easier to compare, and it's the standard way scientists and engineers record measurements across a huge range of sizes.
How do I write a small decimal in scientific notation?
Move the decimal point right until you have one non-zero digit before it, and count the places moved as a negative exponent. For example, 0.00045 becomes 4.5 × 10⁻⁴.
What is the mantissa in scientific notation?
The mantissa is the decimal number in front of the ×10ᵏ part. It must always be at least 1 and less than 10, such as the 9.3 in 9.3 × 10⁷.
How do I convert scientific notation back to a normal number?
Move the decimal point in the mantissa the number of places shown by the exponent — right for a positive exponent, left for a negative one.
