Scientific Notation Converter
Convert between decimals and scientific notation.
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Scientific notation (also called standard form) writes a number as a value between 1 and 10 multiplied by a power of ten — a compact way to handle very large or very small numbers. Type a plain number to convert it, or type scientific notation to expand it back to a decimal.
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How Scientific Notation Works — The Quick Answer
Write the number as one non-zero digit before the decimal point, times a power of ten. The exponent is how many places the point moved: positive for big numbers, negative for small ones.
Shortcut
number = a × 10ⁿ, where 1 ≤ |a| < 10 and n = places the decimal point moved
Both directions
| Decimal | Scientific notation | E-notation |
|---|---|---|
| 123,000 | 1.23 × 10^5 | 1.23e+5 |
| 0.00042 | 4.2 × 10^-4 | 4.2e-4 |
| 299,792,458 | 2.99792458 × 10^8 | 2.99792458e+8 |
| 0.000000001 | 1 × 10^-9 | 1e-9 |
A positive exponent means a large number (move the point right); a negative exponent means a small number (move the point left). The exponent is simply the count of places the decimal point shifts to return to the original number.
How It Works
The Method
Coefficient and exponent
Formula
number = a × 10ⁿ 1 ≤ |a| < 10 n = number of places the decimal point is shifted
Variables
The digits
A single non-zero digit before the decimal point, followed by the rest of the significant digits. For 123,000 the coefficient is 1.23; for 0.00042 it is 4.2.
The power of ten
How many places the decimal point moved. Moving left (for large numbers) gives a positive exponent; moving right (for small numbers) gives a negative one. 123,000 → the point moves 5 places left → 10^5.
The calculator form
Computers and calculators write × 10ⁿ as 'e', so 1.23 × 10^5 becomes 1.23e+5 and 4.2 × 10^-4 becomes 4.2e-4. It means exactly the same thing.
Note: Scientific notation also makes the number of significant figures explicit: 1.23 × 10^5 clearly shows three significant figures, whereas '123000' is ambiguous about whether the trailing zeros count.
Worked Example
123,000 and 0.00042
123,000 → coefficient
Place the decimal after the first digit: 1.23. Drop the trailing zeros.
123,000 → exponent
The point moved 5 places to the left, so the exponent is +5: 1.23 × 10^5.
0.00042 → coefficient and exponent
Move the point right until one non-zero digit is in front: 4.2. That took 4 moves to the right, so the exponent is −4: 4.2 × 10^-4.
Reference Guide
| unit | value | note |
|---|---|---|
| 123,000 | 1.23 × 10^5 | large number |
| 0.00042 | 4.2 × 10^-4 | small number |
| 299,792,458 | 2.99792458 × 10^8 | speed of light, m/s |
Key Features
Last updated: October 5, 2026
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Frequently Asked Questions
How do you write a number in scientific notation?
Move the decimal point so that exactly one non-zero digit sits in front of it — that gives the coefficient (a value between 1 and 10). Then the exponent is the number of places you moved the point: positive if you moved left (a large number), negative if you moved right (a small number). So 123,000 becomes 1.23 × 10^5.
What does the 'e' mean on a calculator (like 1.23e5)?
E-notation is how calculators and computers write 'times ten to the power of'. '1.23e5' means 1.23 × 10^5 = 123,000, and '4.2e-4' means 4.2 × 10^-4 = 0.00042. The 'e' stands for exponent, not the mathematical constant e.
Is scientific notation the same as standard form?
Yes. 'Standard form' is the common name in UK and many Commonwealth maths curricula for what is called 'scientific notation' in the US. Both mean writing a number as a coefficient between 1 and 10 multiplied by a power of ten.
Why is scientific notation useful?
It makes extremely large or small numbers manageable and unambiguous. The speed of light (299,792,458 m/s) becomes 2.99792458 × 10^8, and tiny quantities like 0.000000001 become 1 × 10^-9. It also makes the number of significant figures explicit, which matters in science and engineering.