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.