Convert between standard form, scientific notation, engineering notation and E notation — and calculate with them.
Scientific notation writes a number as a value between 1 and 10 multiplied by a power of ten. The speed of light, 299,792,458 m/s, becomes 2.99792458 × 10⁸. It makes very large and very small numbers readable, and shows precision clearly. Enter a number below to convert it, or switch modes to calculate with two values in scientific notation.
You can type E notation directly, such as 2.998E8 or 1.6e-19. Commas and spaces are ignored.
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Scientific notation, also called standard form in British and Australian schools, expresses any number as a coefficient multiplied by a power of ten.
The value m is the mantissa or coefficient, and n is the exponent. The exponent counts how many places the decimal point moves: positive for large numbers, negative for small ones.
It exists because writing 0.000000000000000000160217663 coulombs is error-prone and hard to read, while 1.60217663 × 10⁻¹⁹ is neither.
Reverse the process. A positive exponent moves the decimal point right, filling with zeros; a negative exponent moves it left. So 6.5 × 10⁴ becomes 65,000, and 3.2 × 10⁻³ becomes 0.0032.
| Notation | Rule | 123,456 becomes | Used by |
|---|---|---|---|
| Scientific | 1 ≤ |m| < 10, any exponent | 1.23456 × 10⁵ | Science, mathematics |
| Engineering | Exponent is a multiple of 3 | 123.456 × 10³ | Engineering, electronics |
| E notation | Same as scientific, typed flat | 1.23456E5 | Calculators, spreadsheets, code |
| Standard form | The ordinary written number | 123,456 | Everyday use |
Why engineering notation exists. Restricting the exponent to multiples of three lines it up with the SI prefixes — kilo (10³), mega (10⁶), giga (10⁹), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹). A resistance of 4.7 × 10³ Ω reads naturally as 4.7 kΩ, which is how it would be written on a circuit diagram.
A note on terminology. In the United States, "standard form" usually means the ordinary written number, as used on this page. In the UK and Australia, "standard form" is often the name for scientific notation itself. If a question seems contradictory, this is usually why.
Multiplying and dividing are straightforward: multiply or divide the mantissas, then add or subtract the exponents. If the result's mantissa falls outside 1 to 10, adjust the exponent to normalise it.
Adding and subtracting need a common exponent first, exactly like finding a common denominator with fractions. To add 1.2 × 10³ and 3.4 × 10², rewrite the second as 0.34 × 10³, then add the mantissas: 1.54 × 10³.
One of the strengths of scientific notation is that it makes precision unambiguous. Written as 1200, you cannot tell whether the zeros are measured or just placeholders. Written as 1.2 × 10³ it clearly has two significant figures; as 1.200 × 10³ it clearly has four.
| Rule | Example | Significant figures |
|---|---|---|
| All non-zero digits count | 123 | 3 |
| Zeros between digits count | 1002 | 4 |
| Leading zeros never count | 0.00120 | 3 |
| Trailing zeros after a point count | 1.200 | 4 |
| Trailing zeros in a plain integer are ambiguous | 1200 | 2 to 4 — write it in scientific notation to be clear |
| In scientific notation, the mantissa says it all | 6.022 × 10²³ | 4 |
This calculator counts significant figures using the conservative reading: trailing zeros in a plain whole number are not counted, because they may only be placeholders. If they are genuinely measured, write the value in scientific notation to remove the ambiguity.
| Quantity | Standard form | Scientific notation |
|---|---|---|
| Speed of light | 299,792,458 m/s | 2.99792458 × 10⁸ |
| Avogadro's number | 602,214,076,000,000,000,000,000 | 6.02214076 × 10²³ |
| Earth's mass | 5,972,000,000,000,000,000,000,000 kg | 5.972 × 10²⁴ |
| Distance to the Sun | 149,600,000,000 m | 1.496 × 10¹¹ |
| Electron charge | 0.000000000000000000160217663 C | 1.60217663 × 10⁻¹⁹ |
| Planck constant | 0.000000000000000000000000000000000662607015 | 6.62607015 × 10⁻³⁴ |
| Mass of a proton | 0.00000000000000000000000000167262 kg | 1.67262 × 10⁻²⁷ |
| Width of a human hair | 0.00007 m | 7 × 10⁻⁵ |
| One nanometre | 0.000000001 m | 1 × 10⁻⁹ |
| World population (approx) | 8,000,000,000 | 8 × 10⁹ |
The full range of SI prefixes, from yocto to yotta — 48 orders of magnitude. Each step of three exponents is a thousandfold change.
| Power | Decimal value | Prefix | Symbol | Example |
|---|---|---|---|---|
| 10²⁴ | 1,000,000,000,000,000,000,000,000 | yotta | Y | Mass of Earth ≈ 6 YKg |
| 10²¹ | 1,000,000,000,000,000,000,000 | zetta | Z | Global data created per year |
| 10¹⁸ | 1,000,000,000,000,000,000 | exa | E | Exascale supercomputing |
| 10¹⁵ | 1,000,000,000,000,000 | peta | P | Large data centre storage |
| 10¹² | 1,000,000,000,000 | tera | T | Terabyte hard drive |
| 10⁹ | 1,000,000,000 | giga | G | Gigahertz processor |
| 10⁶ | 1,000,000 | mega | M | Megapixel camera |
| 10³ | 1,000 | kilo | k | Kilometre, kilogram |
| 10⁰ | 1 | — | — | The base unit |
| 10⁻³ | 0.001 | milli | m | Millimetre, millisecond |
| 10⁻⁶ | 0.000001 | micro | µ | Micrometre, bacteria size |
| 10⁻⁹ | 0.000000001 | nano | n | Nanometre, DNA width |
| 10⁻¹² | 0.000000000001 | pico | p | Picofarad capacitor |
| 10⁻¹⁵ | 0.000000000000001 | femto | f | Femtosecond laser pulse |
| 10⁻¹⁸ | 0.000000000000000001 | atto | a | Attosecond, electron motion |
| 10⁻²¹ | 0.000000000000000000001 | zepto | z | Zeptosecond, light crossing a molecule |
| 10⁻²⁴ | 0.000000000000000000000001 | yocto | y | Yoctogram, mass of a proton ≈ 1.7 yg |
Because engineering notation keeps the exponent at a multiple of three, it maps straight onto these prefixes. The calculator shows the prefix form automatically for any value in range.
| Plain value | Engineering notation | With prefix | Typical use |
|---|---|---|---|
| 0.000001 | 1 × 10⁻⁶ | 1 µ (micro) | 1 µF capacitor |
| 0.001 | 1 × 10⁻³ | 1 m (milli) | 1 mA current |
| 1,000 | 1 × 10³ | 1 k (kilo) | 1 kΩ resistor |
| 4,700 | 4.7 × 10³ | 4.7 k | 4.7 kΩ resistor |
| 1,000,000 | 1 × 10⁶ | 1 M (mega) | 1 MHz frequency |
| 2,400,000,000 | 2.4 × 10⁹ | 2.4 G (giga) | 2.4 GHz Wi-Fi |
This is why an electronics component is labelled 4.7 kΩ rather than 4,700 Ω, and why file sizes jump from megabytes to gigabytes to terabytes — each step is exactly 10³.
Computers store decimal numbers in the IEEE 754 binary floating-point format, and some values that look simple in decimal cannot be represented exactly in binary. One tenth is the classic example: 0.1 has no exact binary form, which is why 0.1 + 0.2 famously gives 0.30000000000000004 in most programming languages.
This calculator cleans results to twelve significant figures, which removes that visible noise while keeping every digit you are entitled to. It also decomposes numbers using exact exponential formatting rather than logarithms, so the mantissa lands correctly even at exact powers of ten. If you need arithmetic with no binary approximation at all, our Big Number Calculator uses exact integer arithmetic, and the Decimal Calculator uses exact decimal arithmetic.
Distances between stars are impossible to write out, so powers of ten are standard.
1 light year ≈ 9.46 × 10¹⁵ mFundamental constants span dozens of orders of magnitude in both directions.
h = 6.626 × 10⁻³⁴ J·sA mole contains Avogadro's number of particles, far beyond ordinary notation.
6.022 × 10²³ /molFloating-point numbers are stored as a mantissa and an exponent — scientific notation in binary.
1.6e-19Component values use engineering notation, matching the SI prefixes on the part.
4.7 kΩ = 4.7 × 10³Cell and virus sizes, and population counts, both need powers of ten.
virus ≈ 1 × 10⁻⁷ mNational debt and GDP figures are easier to compare as orders of magnitude.
$2.6 × 10¹²Very small p-values and very large record counts both appear in E notation.
p = 1.2e-81) 4.5 × 10⁴ 2) 3.2 × 10⁻³ 3) 65,000 4) 0.002 5) three
1) 1 × 10⁴ 2) 4 × 10³ 3) 1.54 × 10³ 4) 123.456 × 10³ 5) 4.7 × 10⁶
What is scientific notation?
Scientific notation writes a number as a value between 1 and 10 multiplied by a power of ten. For example, 299,792,458 becomes 2.99792458 times 10 to the power 8.
How do you convert a number to scientific notation?
Move the decimal point until one non-zero digit remains in front of it, then count the places you moved. Moving left gives a positive exponent and moving right gives a negative one.
How do you convert scientific notation back to a normal number?
Move the decimal point by the number of places the exponent gives. A positive exponent moves it right and a negative exponent moves it left, filling with zeros as needed.
What is the mantissa?
The mantissa, also called the coefficient, is the number in front of the power of ten. In proper scientific notation it is at least 1 and less than 10.
What is E notation?
E notation is scientific notation typed on one line, where E stands for times ten to the power. Calculators and spreadsheets show 1.6 times 10 to the minus 19 as 1.6E-19.
What is engineering notation?
Engineering notation is like scientific notation but the exponent must be a multiple of three. This lines it up with SI prefixes such as kilo, mega and milli.
What is the difference between scientific and engineering notation?
Scientific notation keeps the mantissa between 1 and 10, while engineering notation allows it up to 1000 so the exponent stays a multiple of three. 123,456 is 1.23456 times 10 to the 5 in scientific, but 123.456 times 10 cubed in engineering.
What is standard form?
In the United States standard form usually means the ordinary written number. In the UK and Australia, standard form is often another name for scientific notation itself, so it is worth checking which meaning a question intends.
How do you multiply numbers in scientific notation?
Multiply the mantissas and add the exponents. So 3 times 10 to the 8, multiplied by 2 times 10 to the 5, gives 6 times 10 to the 13.
How do you divide numbers in scientific notation?
Divide the mantissas and subtract the exponents. So 6 times 10 to the 23, divided by 2 times 10 to the 10, gives 3 times 10 to the 13.
How do you add numbers in scientific notation?
Rewrite them so both have the same exponent, then add the mantissas. To add 1.2 times 10 cubed and 3.4 times 10 squared, rewrite the second as 0.34 times 10 cubed, giving 1.54 times 10 cubed.
Why is scientific notation useful?
It makes very large and very small numbers readable, shows the order of magnitude at a glance, states precision unambiguously, and makes multiplication and division much easier.
What are significant figures?
Significant figures are the digits that carry real information about precision. In scientific notation every digit of the mantissa is significant, which removes the ambiguity of trailing zeros.
How many significant figures does 1200 have?
It is ambiguous, and could be two, three or four depending on how the value was measured. Writing it as 1.2 times 10 cubed or 1.200 times 10 cubed makes the precision clear.
Can the mantissa be negative?
Yes. A negative number keeps its sign in the mantissa, so minus 4560 becomes minus 4.56 times 10 cubed. The exponent controls size, not sign.
Why must the mantissa be between 1 and 10?
So that every number has exactly one correct representation. Without the rule, 1200 could be written as 12 times 10 squared or 0.12 times 10 to the fourth, making values harder to compare.
How do you write zero in scientific notation?
Zero has no standard scientific notation, because no power of ten multiplied by a non-zero mantissa equals zero. It is simply written as 0.
What does a negative exponent mean?
A negative exponent means the number is smaller than 1. Ten to the power minus 3 is one thousandth, so 3.2 times 10 to the minus 3 is 0.0032.
How is scientific notation used in science?
Astronomy uses it for distances, chemistry for the number of particles in a mole, and physics for constants such as the Planck constant, which spans dozens of orders of magnitude.
How is scientific notation used in computing?
Floating-point numbers are stored as a mantissa and an exponent, which is scientific notation in binary. Programming languages and spreadsheets display very large or very small values in E notation.
Is this Scientific Notation Calculator free?
Yes. It is free with no sign-up, works on any device, and runs entirely in your browser so your entries stay private.