What is scientific notation?
Scientific notation is a compact way to write extremely large or extremely small numbers. A non-zero number is expressed as a × 10n, where the coefficient satisfies 1 ≤ |a| < 10 and the exponent n tells you the order-of-magnitude scale.
Instead of counting a long string of zeros, scientific notation separates a number into two ideas: how large the significant digits are and how far the decimal point must move. This makes measurements easier to read, compare, multiply, divide, and communicate.
Large numbers
Positive exponents mean the decimal point moves to the right when you return to ordinary form.
Small numbers
Negative exponents mean the decimal point moves to the left when you return to ordinary form.
How to convert a number to scientific notation
To convert a decimal number, move the decimal point until exactly one non-zero digit remains to its left. Count the moves. A move to the left produces a positive exponent; a move to the right produces a negative exponent. The result is then normalized to the scientific-notation form.
Find the first non-zero digit
That digit becomes the first digit of the coefficient.
Place the decimal
Leave one non-zero digit on the left side of the decimal point.
Count the moves
Count every place the decimal point crossed from its original position.
Assign the sign
Left means positive; right means negative; no move means zero.
How to convert scientific notation to decimal form
Read the exponent as a movement instruction. For a positive exponent, move the decimal point to the right. For a negative exponent, move it to the left. If you run out of written digits, fill the remaining places with zeros.
3.456 × 105
The decimal point moves five places to the right.
5.600 × 10−3
The negative exponent tells us to move the decimal point three places to the left.
7.2 × 100
An exponent of zero means the value is already on the ×10⁰ scale.
−8.4 × 104
The sign belongs to the coefficient; the exponent still controls place value.
Scientific notation worked examples
These examples change the scale, the sign, or the operation so you can see exactly what the exponent is doing.
357,096 → scientific notation
The decimal point moved five places to the left.
0.005600 → scientific notation
Three places to the right gives the negative exponent.
4.5 × 10⁴ → decimal
Four powers of ten move the decimal point four places right.
7.2 × 10⁻⁶ in E notation
E notation is a compact computer-friendly spelling of the same power-of-ten expression.
Scientific notation formulas and operations
Scientific notation is particularly useful when multiplying, dividing, adding, or subtracting numbers with very different scales. The key is knowing which parts of the expression combine directly.
Multiplication
Multiply the coefficients and add the exponents. If the coefficient falls outside the range 1 to less than 10, normalize the result and adjust the exponent.
Worked example: (2.4 × 105)(3 × 107) = 7.2 × 1012.
Division
Divide the coefficients and subtract the exponents. Normalize the coefficient if necessary.
Worked example: (8.4 × 109) ÷ (2 × 103) = 4.2 × 106.
Addition and subtraction
You cannot simply add the coefficients when the exponents differ. First rewrite the numbers so they use the same power of ten.
=(1.432 + 0.8 − 1) × 102
=1.232 × 102
| Operation | Coefficient rule | Exponent rule | Final check |
|---|---|---|---|
| Multiply | a × b | n + m | Normalize |
| Divide | a ÷ b | n − m | Normalize |
| Add | Make exponents match | Use common exponent | Then normalize |
| Subtract | Make exponents match | Use common exponent | Then normalize |
Engineering notation and SI prefixes
Engineering notation is closely related to scientific notation, but it constrains the exponent to multiples of 3. That makes the coefficient connect naturally to SI prefixes such as kilo (103), mega (106), milli (10−3), micro (10−6), and nano (10−9).
| Prefix | Symbol | Power | Factor |
|---|---|---|---|
| giga | G | 10⁹ | 1,000,000,000 |
| mega | M | 10⁶ | 1,000,000 |
| kilo | k | 10³ | 1,000 |
| base | — | 10⁰ | 1 |
| milli | m | 10⁻³ | 0.001 |
| micro | μ | 10⁻⁶ | 0.000001 |
| nano | n | 10⁻⁹ | 0.000000001 |
E notation, significant figures, and computer-friendly numbers
E notation replaces “× 10n” with the letter e. For example, 6.022 × 1023 becomes 6.022e23. It is widely used in calculators, spreadsheets, programming languages, scientific data, and machine-readable text.
Same value, different notation
Scientific notation
E notation
Significant figures still matter
The trailing zeros communicate four significant figures when measurement precision makes them meaningful.
Where is scientific notation used?
Scientific notation is not just a classroom format. It is a practical language for quantities spanning many orders of magnitude. Astronomy uses it for distances, masses, and star populations; physics uses it for constants, particle masses, energy, and wavelengths; chemistry uses it for molecule counts and atomic-scale measurements; and engineering uses it for electrical, mechanical, and signal quantities.
Scientific notation reference table
| Decimal form | Scientific notation | E notation | Engineering notation |
|---|---|---|---|
| 1 | 1 × 10⁰ | 1e0 | 1 × 10⁰ |
| 1,000 | 1 × 10³ | 1e3 | 1 × 10³ |
| 72,000 | 7.2 × 10⁴ | 7.2e4 | 72 × 10³ |
| 1,349.12 | 1.34912 × 10³ | 1.34912e3 | 1.34912 × 10³ |
| 0.000000435 | 4.35 × 10⁻⁷ | 4.35e-7 | 435 × 10⁻⁹ |
| −7,500 | −7.5 × 10³ | −7.5e3 | −7.5 × 10³ |
| −0.00005234 | −5.234 × 10⁻⁵ | −5.234e-5 | −52.34 × 10⁻⁶ |
Scientific notation calculator FAQ
It is a normalized representation of a number as a coefficient times a power of ten, usually with 1 ≤ |a| < 10.
A negative exponent means the value is on a small scale and the decimal point moves to the left when you convert back to decimal form.
Scientific notation uses any integer exponent with a coefficient from 1 up to but not including 10. Engineering notation restricts the exponent to multiples of 3.
It represents the same mathematical idea using e instead of “× 10^”. For example, 3.2 × 10⁶ and 3.2e6 have the same value.
First convert them to the same power of ten, add or subtract the coefficients, and then normalize the result if necessary.
The calculator keeps the entered decimal digits as text instead of forcing very large values through binary floating-point arithmetic. This helps preserve long strings of significant digits during conversion.
The coefficient is where significant digits are normally shown. Changing the number of significant figures changes the displayed precision without changing the intended scale represented by the exponent.