Enter a number to convert it to scientific notation, or use Multiply/Divide mode.
Scientific Notation Format & Rules
Scientific notation writes a number as a coefficient of at least 1 and less than 10, times a power of 10: 299,792,458 = 2.99792458 × 108, and 0.00042 = 4.2 × 10−4. Type any number above to convert it and see its E-notation, standard form and significant figures, or switch modes to multiply and divide.
Scientific notation expresses any number as a × 10^n, where 1 ≤ |a| < 10 (the coefficient) and n is an integer (the exponent). It is the universal standard in science and engineering for expressing very large and very small numbers without writing dozens of zeros.
In E-notation (used in calculators and code): 2.998E8 = 2.998 × 10^8. This is identical in meaning but more compact for digital display.
Converting to Scientific Notation
Multiplying in Scientific Notation
Dividing in Scientific Notation
Large Number Reference
Conversion Examples at a Glance
A positive exponent means a number of 10 or more, a negative exponent means a number below 1, and exponent 0 covers 1 up to 10.
| Standard form | Scientific notation | E-notation |
|---|---|---|
| 602,200,000,000,000,000,000,000 | 6.022 × 1023 | 6.022E23 |
| 1,230,000 | 1.23 × 106 | 1.23E6 |
| 45,000 | 4.5 × 104 | 4.5E4 |
| 5,280 | 5.28 × 103 | 5.28E3 |
| 1 | 1 × 100 | 1E0 |
| 0.1 | 1 × 10−1 | 1E−1 |
| 0.0056 | 5.6 × 10−3 | 5.6E−3 |
| 0.00072 | 7.2 × 10−4 | 7.2E−4 |
| 0.000000308 | 3.08 × 10−7 | 3.08E−7 |
| −32,000 | −3.2 × 104 | −3.2E4 |
Significant Figures in Scientific Notation
Scientific notation is the cleanest way to show how precise a number is, because every digit in the coefficient counts. The rules for counting:
- All nonzero digits count, and so do zeros between them (1,020 has at least 3).
- Leading zeros never count: 0.00450 has 3 (the 4, the 5 and the final 0).
- Trailing zeros after a decimal point count: 300.0 has 4.
- Trailing zeros in a whole number with no decimal point are ambiguous: 4,500 could have 2, 3 or 4. Scientific notation removes the doubt.
| Number | Significant figures | Scientific notation |
|---|---|---|
| 0.00450 | 3 | 4.50 × 10−3 |
| 300.0 | 4 | 3.000 × 102 |
| 6.0200 | 5 | 6.0200 × 100 |
| 0.000308 | 3 | 3.08 × 10−4 |
| 1,020 | 3 to 4 (ambiguous) | 1.02 × 103 or 1.020 × 103 |
| 4,500 | 2 to 4 (ambiguous) | 4.5 × 103, 4.50 × 103 or 4.500 × 103 |
When you multiply or divide, round the answer to the fewest significant figures in the inputs. (3.0 × 104) × (2.51 × 103) = 7.53 × 107, which rounds to 7.5 × 107 because 3.0 has only two. The calculator shows this rounded answer in the significant figures row.
Worked Examples and Common Mistakes
Multiplying: (4.5 × 106) × (3.0 × 10−4)
Multiply the coefficients, 4.5 × 3.0 = 13.5, and add the exponents, 6 + (−4) = 2. That gives 13.5 × 102. The coefficient is above 10, so move the point one place left and add 1 to the exponent: 1.35 × 103, or 1.4 × 103 to two significant figures.
Dividing: (2.4 × 103) ÷ (6.0 × 107)
2.4 ÷ 6.0 = 0.4 and 3 − 7 = −4, giving 0.4 × 10−4. The coefficient is below 1, so move the point one place right and subtract 1 from the exponent: 4.0 × 10−5, which is 0.000040.
Mistakes to avoid
- Leaving the coefficient out of range. 12 × 103 and 0.5 × 103 are correct values but not proper scientific notation. Write 1.2 × 104 and 5 × 102.
- Getting the exponent sign backwards. 0.004 is 4 × 10−3, not 4 × 103. Numbers below 1 always have a negative exponent.
- Mixing up a negative number and a negative exponent. −3.2 × 104 is −32,000. 3.2 × 10−4 is 0.00032, a small positive number.
- Adding without a common exponent. (3 × 105) + (4 × 104) is 3.4 × 105, not 7 × 109. Rewrite one number so both have the same power of 10 first.
- Reading E as the constant e. 2.5E3 means 2.5 × 103 = 2,500. It has nothing to do with e = 2.71828.
For raising numbers to any power, including powers of 10, use the exponent calculator. The log calculator gives the base 10 logarithm, which is the exponent in scientific notation plus the log of the coefficient.
Method and sources. Numbers are normalised so the coefficient is at least 1 and less than 10, using the exact decimal expansion of the value, and standard form is written out digit by digit. Significant figure rules follow standard scientific and engineering convention. Avogadro constant 6.02214076 × 1023 per mole (exact since the 2019 SI redefinition), shown here as 6.022 × 1023. Every value in the tables and examples above was computed and checked.
Scientific Notation Questions
What is scientific notation?
Scientific notation expresses numbers as a × 10^n, where 1 ≤ |a| < 10. Example: 93,000,000 miles (Earth-Sun distance) = 9.3 × 10^7. 0.000000001 = 1 × 10^−9. It makes very large and very small numbers manageable and immediately communicates the order of magnitude. It is the standard in science, engineering, astronomy, and physics.
How do I convert a number to scientific notation?
(1) Move the decimal point so exactly one non-zero digit is to its left. (2) Count the places moved: that is the exponent. Moving left gives a positive exponent; moving right gives a negative exponent. (3) Write in the form a × 10^n. Example: 0.0045. Move right 3 places: 4.5. Exponent: −3. Result: 4.5 × 10^−3.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. (3 × 10^4) × (5 × 10^6) = (3 × 5) × 10^(4+6) = 15 × 10^10. If the resulting coefficient is ≥10 or <1, adjust: 15 × 10^10 = 1.5 × 10^11. This adjustment keeps the result in proper scientific notation form.
How do I divide numbers in scientific notation?
Divide the coefficients and subtract the exponents. (8 × 10^9) ÷ (4 × 10^3) = (8/4) × 10^(9−3) = 2 × 10^6. If the coefficient falls outside 1≤|a|<10, adjust. Example: (3 × 10^5) ÷ (6 × 10^2) = 0.5 × 10^3 = 5 × 10^2. The subtraction of exponents makes division of very large numbers straightforward.
What is E-notation?
E-notation (used in calculators, spreadsheets, and programming languages) replaces "× 10^" with "E". 2.998E8 = 2.998 × 10^8 = 299,800,000. 4.5E−3 = 4.5 × 10^−3 = 0.0045. E-notation is identical in meaning to standard scientific notation, just more compact for digital display. In Python, JavaScript, and most programming languages, E-notation is the standard way to write scientific numbers in code.
How do I add numbers in scientific notation?
Convert both to the same exponent first, then add the coefficients. (3 × 10^5) + (4 × 10^4) = (3 × 10^5) + (0.4 × 10^5) = 3.4 × 10^5. This is why addition/subtraction in scientific notation is more involved than multiplication/division: you need a common exponent before combining. Alternatively, convert both to standard notation, add, then convert back.
What are common examples of scientific notation in science?
Speed of light: 2.998 × 10^8 m/s. Distance from Earth to Sun: 1.496 × 10^11 m. Mass of an electron: 9.109 × 10^−31 kg. Avogadro's number: 6.022 × 10^23 mol^−1. Planck's constant: 6.626 × 10^−34 J·s. Charge of an electron: 1.602 × 10^−19 C. Scientific notation is the only practical way to write these quantities.
What is a googol and how does it relate to scientific notation?
A googol is 10^100: a 1 followed by 100 zeros. In scientific notation: 1 × 10^100. A googolplex is 10^(10^100). The estimated number of atoms in the observable universe is approximately 10^80: far less than a googol. The company "Google" was named after "googol." Scientific notation lets us meaningfully compare these astronomical numbers and see their relative sizes at a glance.
What is the difference between significant figures and scientific notation?
Significant figures indicate precision: how many digits are meaningful. Scientific notation makes significant figures explicit: 3.00 × 10^8 has 3 significant figures; 3 × 10^8 has 1. In standard notation, 300 is ambiguous (1, 2, or 3 sig figs?). Scientific notation resolves this ambiguity. Scientists use scientific notation partly to communicate precision unambiguously alongside magnitude.
How do I convert from scientific notation back to standard form?
Move the decimal point in the coefficient the number of places indicated by the exponent. Positive exponent: move right (large number). Negative exponent: move left (small number). Examples: 3.45 × 10^4 = 34,500 (move decimal right 4 places). 2.1 × 10^−3 = 0.0021 (move decimal left 3 places). Fill in zeros as needed.
How do you write a negative number in scientific notation?
Put the minus sign in front of the coefficient and convert the rest as usual. −45,000 = −4.5 × 104 and −0.0023 = −2.3 × 10−3. The sign of the number and the sign of the exponent are separate: the first tells you whether the value is below zero, the second tells you whether its size is above or below 1.
How do I enter scientific notation on a calculator or in Excel?
On most scientific calculators use the EE or EXP key: 6.022 EE 23 enters 6.022 × 1023. In Excel, Google Sheets and most programming languages, type it with an E: 6.022E23 or 4.5E−3. Excel shows numbers in this form in the Scientific cell format, and switches to it automatically when a value is too wide for its column.