How to use the scientific notation calculator
- Choose a mode. “Convert a number” rewrites one number in every notation. “Multiply, divide, add” works with two numbers.
- Type the number in any common form. The calculator reads plain decimals with or without commas (37,000 or 0.0052), e-notation (3.7e4 or 5.2E-3), and powers of ten written as 3.7 × 10^4, 3.7x10^4 or 3.7*10**4.
- Pick significant figures if you need them. “Keep all digits” shows exactly what you typed. Choosing 2 to 6 rounds the scientific, e-notation and engineering results.
- Read the results. The large figure is scientific notation, with a note on how far the decimal point moved. Below it you’ll see e-notation, engineering notation with the matching SI prefix, and the number written out in standard form.
In convert mode, the calculator also counts the significant figures in the number as you typed it.
What scientific notation is
A number is in scientific notation when it is written as a × 10ⁿ, where a is at least 1 and less than 10 and n is a whole number. OpenStax’s Prealgebra 2e (section 10.5) gives the steps: move the decimal point so that only one nonzero digit is to its left, count how many places you moved it, and use that count as the exponent. Moving left gives a positive exponent; moving right gives a negative one.
- 37,000: move the point 4 places left → 3.7 × 10⁴.
- 0.0052: move the point 3 places right → 5.2 × 10⁻³.
To go back to standard form, move the point by the exponent: right for a positive exponent, left for a negative one, filling with zeros.
- 6.2 × 10³ = 6,200.
- 8.9 × 10⁻² = 0.089.
These four examples are the textbook’s Examples 10.74 to 10.77, and the calculator reproduces each of them.
Multiplying, dividing, adding and subtracting
Multiply the a parts and add the exponents. (4 × 10⁵)(2 × 10⁻⁷) = 8 × 10⁻², which is 0.08.
Divide the a parts and subtract the exponents. (9 × 10³) ÷ (3 × 10⁻²) = 3 × 10⁵, which is 300,000.
If the a part ends up outside 1 to 10, adjust it: (5 × 10³)(4 × 10²) = 20 × 10⁵ = 2 × 10⁶.
Add or subtract by first rewriting both numbers with the same exponent. 3.2 × 10⁴ + 5 × 10³ becomes 3.2 × 10⁴ + 0.5 × 10⁴ = 3.7 × 10⁴. When the exponents are far apart, the smaller number barely matters: adding 1 to 10¹⁵ changes the 16th significant digit.
In arithmetic mode the result is computed to about 12 significant digits, then shown in every notation. That is plenty for coursework and lab reports and hides the tiny binary rounding errors that make some calculators show 0.1 + 0.2 as 0.30000000000000004.
E-notation and engineering notation
E-notation is how calculators, spreadsheets and programming languages display scientific notation: 3.7e+4 means 3.7 × 10⁴ and 5.2e-3 means 5.2 × 10⁻³. The letter E stands for “times ten to the.” It is not Euler’s number e ≈ 2.718.
Engineering notation keeps the exponent a multiple of 3, so a can range from 1 up to (but not including) 1,000. That matches the SI prefixes, which NIST lists in steps of a thousand from quecto (10⁻³⁰) to quetta (10³⁰). For example:
| Number | Engineering notation | SI prefix |
|---|---|---|
| 37,000 | 37 × 10³ | k (kilo) |
| 4,700,000 | 4.7 × 10⁶ | M (mega) |
| 0.0052 | 5.2 × 10⁻³ | m (milli) |
| 0.000047 | 47 × 10⁻⁶ | µ (micro) |
| 0.000000047 | 47 × 10⁻⁹ | n (nano) |
So 37,000 meters is 37 km, 0.0052 seconds is 5.2 ms, and a 47 × 10⁻⁹ farad capacitor is labeled 47 nF.
Significant figures
Scientific notation makes significant figures unambiguous, which is one reason labs use it. Written as 37,000, a measurement might have 2 significant figures or 5; written as 3.7 × 10⁴ it clearly has 2, and 3.7000 × 10⁴ clearly has 5.
The calculator counts significant figures in what you type using the usual classroom rules: nonzero digits count; zeros between them count; leading zeros, as in 0.0052, don’t; trailing zeros count only when a decimal point is shown. That makes 0.00520 three significant figures, 37000 two, and 37000. (with a trailing point) five.
Rounding is half up. The speed of light, 299,792,458 meters per second, rounds to 3.00 × 10⁸ at three significant figures, and 9.996 rounds to 1.00 × 10¹, carrying into the exponent.
Why conversions here don’t lose digits
Most online converters turn your input into a floating-point number first, which keeps only about 15 to 17 significant digits. This calculator converts the digits as text, so a long value such as 123,456.789012345678 keeps all 18 digits in every notation. Only the arithmetic mode uses floating point.
Common mistakes
- Reading a negative exponent as a negative number. 5.2 × 10⁻³ is a small positive number, 0.0052. A negative number has the minus sign in front: −5.2 × 10³ is −5,200.
- Leaving the first part outside 1 to 10. 37 × 10³ equals 37,000, but it is engineering notation, not scientific notation. Move the point one more place and add one to the exponent to get 3.7 × 10⁴.
- Typing “× 10” on a calculator with an EE key. On many handheld calculators, the EE or EXP key already means “× 10 to the.” Pressing 3.7 × 10 EE 4 enters 3.7 × 10 × 10⁴, which is ten times too large.
- Adding exponents when you add numbers. Exponents add only when you multiply. 2 × 10³ + 3 × 10³ is 5 × 10³, not 5 × 10⁶.
- Dropping significant zeros. A measured 2.50 × 10⁻² meters is not the same report as 2.5 × 10⁻² meters; the trailing zero says the measurement was good to the thousandth of a meter.
Numbers you’ll meet in science classes
The Avogadro constant is 6.02214076 × 10²³ per mole, an exact value since the SI was redefined in 2019. The speed of light is 299,792,458 meters per second, often rounded to 3.00 × 10⁸ m/s. Both are presets in the calculator, so you can see how they look in e-notation and engineering notation. Small values work the same way: a wavelength of 0.00000055 meters is 5.5 × 10⁻⁷ m in scientific notation and 550 × 10⁻⁹ m, or 550 nm, in engineering notation.
Sources & assumptions
How this calculator gets its numbers. Full method: our methodology.
- Scientific notation is a × 10ⁿ with 1 ≤ |a| < 10; engineering notation uses an exponent that is a multiple of 3, matched to its SI prefix.
- Conversions work on the digits you type, so nothing is lost to floating-point rounding; arithmetic is computed to about 12 significant digits.
- Significant figures typed: trailing zeros count only when a decimal point is shown (37000 has 2, 37000. has 5); rounding is half up.
Sources
- OpenStax (Rice University), Prealgebra 2e, 10.5 Integer Exponents and Scientific Notation. a × 10ⁿ with 1 ≤ a < 10, with Examples 10.74 to 10.79: 37,000 = 3.7 × 10⁴, 0.0052 = 5.2 × 10⁻³, 6.2 × 10³ = 6,200, 8.9 × 10⁻² = 0.089, (4 × 10⁵)(2 × 10⁻⁷) = 0.08 and (9 × 10³) ÷ (3 × 10⁻²) = 300,000.
- National Institute of Standards and Technology, Metric (SI) Prefixes. The 24 SI prefixes from quetta (10³⁰) to quecto (10⁻³⁰), including kilo (10³), mega (10⁶), milli (10⁻³) and micro (10⁻⁶).
Last reviewed . In lab work, round the final answer to the significant figures your measurements support.
Frequently asked questions
How do I write a number in scientific notation?
Move the decimal point until one nonzero digit is to its left, and use the number of places you moved as the exponent of 10. Moving left gives a positive exponent, moving right a negative one. 37,000 = 3.7 × 10⁴.
How do I write a small number like 0.0052 in scientific notation?
Move the decimal point 3 places right to get 5.2, so the exponent is −3: 0.0052 = 5.2 × 10⁻³.
What does 3.7e4 mean?
It is e-notation for 3.7 × 10⁴, or 37,000. Calculators and spreadsheets use E to mean “times ten to the power.”
How do I multiply numbers in scientific notation?
Multiply the decimal parts and add the exponents, then adjust if the decimal part is 10 or more. (4 × 10⁵)(2 × 10⁻⁷) = 8 × 10⁻² = 0.08.
What is the difference between scientific and engineering notation?
Scientific notation keeps one digit before the decimal point. Engineering notation uses exponents that are multiples of 3, matching prefixes like kilo, mega and milli, so 37,000 is 37 × 10³.
How many significant figures does 37,000 have?
Two, by the usual rule that trailing zeros without a decimal point don’t count. Write 3.7000 × 10⁴ or 37,000. if all five digits were measured.