Scientific Notation Calculator

Q: What is the difference between scientific and engineering notation?

Scientific notation always places one digit before the decimal point (1 ≤ |mantissa| < 10). Engineering notation restricts the exponent to multiples of 3 (... -6, -3, 0, 3, 6, 9 ...), which lines up with SI prefixes like micro, milli, kilo, mega. This means the mantissa can range from 1 to 999.999. Engineers prefer this because "47 kΩ" is more practical than "4.7 × 10⁴ Ω."

Q: What does E notation mean?

E notation replaces "× 10ⁿ" with the letter E followed by the exponent. So 3.5 × 10⁸ becomes 3.5E8. This format is used in programming languages (C, Python, JavaScript), spreadsheets (Excel, Google Sheets), and calculator displays because it avoids superscript characters that are hard to type. It means exactly the same thing as scientific notation.

Q: What are significant figures?

Significant figures are the digits that carry meaningful information about a measurement's precision. In 0.00450, the significant figures are 4, 5, and the trailing 0 (three total). Leading zeros are not significant. The calculator lets you choose 2 to 10 significant figures, which controls how many digits appear in the mantissa. More figures = more precision but a longer number.

Q: Can I enter negative numbers?

Yes. Enter -186000 and you get -1.86 × 10⁵. The negative sign applies to the mantissa only. The exponent indicates the magnitude (size), not the sign. A negative exponent means the number is small (between -1 and 1), not that the number itself is negative. For example, -3 × 10⁻⁴ = -0.0003 (negative and small).

Q: Why does the calculator show 10⁰ for numbers between 1 and 10?

Any number raised to the power of 0 equals 1, so 10⁰ = 1. The expression 7.3 × 10⁰ means 7.3 × 1 = 7.3. It looks redundant, but it keeps the notation consistent: every number in scientific notation has the form a × 10ⁿ regardless of its size. The exponent 0 simply means "the decimal point did not need to move."

Q: How large a number can this calculator handle?

JavaScript uses 64-bit floating-point numbers (IEEE 754), which can represent values up to approximately 1.8 × 10³⁰⁸ and down to about 5 × 10⁻³²⁴. Beyond these limits, the number overflows to Infinity or underflows to 0. For exact integer representation, the limit is 2⁵³ (about 9 × 10¹⁵). The calculator handles all numbers within these ranges and shows results in scientific notation with up to 10 significant figures.

What is scientific notation?

Scientific notation expresses any number as a product of two parts: a mantissa between 1 and 10 (exclusive) and a power of 10. The speed of light is 299,792,458 m/s - in scientific notation that becomes 2.998 × 10⁸. The mass of a proton is 0.0000000000000000000000000016726 kg - in scientific notation that is 1.673 × 10⁻²⁷. This calculator converts in both directions: type a number and get the scientific form, or type a mantissa and exponent and get the full number back.

Quick start example

Convert 0.00045 to scientific notation. Select Number Scientific notation, type 0.00045, leave precision at 4 digits, click Convert.
Scientific: 4.5 × 10⁻⁴
Engineering: 450 × 10⁻⁶ (exponent divisible by 3)
SI Prefix: μ (micro)

Three notation formats compared

Format	Rule	Example (186,000)	Used in
Scientific	1 ≤ \|a\| < 10	1.86 × 10⁵	Physics, chemistry, astronomy
Engineering	Exponent divisible by 3	186 × 10³	Electrical engineering, SI units
E notation	Same as scientific, written as aEn	1.86E5	Programming, spreadsheets, calculators

Engineering notation aligns exponents with SI prefixes (kilo = 10³, mega = 10⁶, milli = 10⁻³, micro = 10⁻⁶). This makes it easy to read values with units: 4.7 × 10⁻⁹ F becomes 4.7 nF (nanofarads) without mental conversion.

SI prefix reference table

Prefix	Symbol	Power	Example
yotta	Y	10²⁴	mass of Earth ~6 Yg
tera	T	10¹²	1 TB hard drive
giga	G	10⁹	2.4 GHz WiFi
mega	M	10⁶	5 MP camera
kilo	k	10³	5 km distance
milli	m	10⁻³	500 mL bottle
micro	μ	10⁻⁶	red blood cell ~7 μm
nano	n	10⁻⁹	CPU transistor ~5 nm
pico	p	10⁻¹²	capacitor 100 pF

Practical examples

Example 1 - speed of light
The speed of light is 299,792,458 m/s. Enter this number. Scientific: 2.998 × 10⁸. Engineering: 299.8 × 10⁶. SI prefix: M (mega), meaning roughly 300 megameters per second. The calculator shows all formats at once.

Example 2 - Avogadro constant
Avogadro's number is approximately 6.022 × 10²³. Select Scientific notation Number, enter mantissa 6.022 and exponent 23. The calculator shows the full number: 602,200,000,000,000,000,000,000 - a number so large it has no common SI prefix (yotta = 10²⁴ is the closest).

Example 3 - transistor size
A modern CPU transistor gate is about 0.000000005 meters (5 nm). Enter 0.000000005: scientific notation gives 5 × 10⁻⁹, engineering gives 5 × 10⁻⁹ (already aligned), and SI prefix is n (nano). That is why we say "5 nanometer process."

Example 4 - national debt
If a country's national debt is 33,100,000,000,000 dollars, enter that number. Scientific: 3.31 × 10¹³. Engineering: 33.1 × 10¹². SI prefix: T (tera). In everyday language: 33.1 trillion dollars. The engineering notation makes it immediately clear which "illion" bracket the number falls in.

Example 5 - negative number
Temperature of deep space: approximately -270.45 degrees Celsius (2.7 K). Enter -270.45. Scientific: -2.704 × 10². The sign is preserved. The exponent (2) means the number is in the hundreds range. Negative numbers follow the same rules - only the sign of the mantissa changes.

Example 6 - precision comparison
Enter 123456789 with 2 significant figures: 1.2 × 10⁸. With 4 figures: 1.235 × 10⁸. With 8 figures: 1.2345679 × 10⁸. Increasing precision keeps more original digits in the mantissa but never changes the exponent. Use 2-3 figures for rough estimates and 6-8 for laboratory work.

How the conversion works

To convert a number to scientific notation: find the position of the first non-zero digit. Move the decimal point so that exactly one non-zero digit is to its left. Count how many places you moved it - that becomes the exponent. Moving left gives a positive exponent (the number was large), moving right gives a negative exponent (the number was small).

186,000 move decimal 5 places left 1.86 × 10⁵
0.00045 move decimal 4 places right 4.5 × 10⁻⁴
7.3 already between 1 and 10 7.3 × 10⁰

FAQ

What is the difference between scientific and engineering notation?

Scientific notation always places one digit before the decimal point (1 ≤ |mantissa| < 10). Engineering notation restricts the exponent to multiples of 3 (... -6, -3, 0, 3, 6, 9 ...), which lines up with SI prefixes like micro, milli, kilo, mega. This means the mantissa can range from 1 to 999.999. Engineers prefer this because "47 kΩ" is more practical than "4.7 × 10⁴ Ω."

What does E notation mean?

E notation replaces "× 10ⁿ" with the letter E followed by the exponent. So 3.5 × 10⁸ becomes 3.5E8. This format is used in programming languages (C, Python, JavaScript), spreadsheets (Excel, Google Sheets), and calculator displays because it avoids superscript characters that are hard to type. It means exactly the same thing as scientific notation.

What are significant figures?

Significant figures are the digits that carry meaningful information about a measurement's precision. In 0.00450, the significant figures are 4, 5, and the trailing 0 (three total). Leading zeros are not significant. The calculator lets you choose 2 to 10 significant figures, which controls how many digits appear in the mantissa. More figures = more precision but a longer number.

Can I enter negative numbers?

Yes. Enter -186000 and you get -1.86 × 10⁵. The negative sign applies to the mantissa only. The exponent indicates the magnitude (size), not the sign. A negative exponent means the number is small (between -1 and 1), not that the number itself is negative. For example, -3 × 10⁻⁴ = -0.0003 (negative and small).

Why does the calculator show 10⁰ for numbers between 1 and 10?

Any number raised to the power of 0 equals 1, so 10⁰ = 1. The expression 7.3 × 10⁰ means 7.3 × 1 = 7.3. It looks redundant, but it keeps the notation consistent: every number in scientific notation has the form a × 10ⁿ regardless of its size. The exponent 0 simply means "the decimal point did not need to move."

How large a number can this calculator handle?

JavaScript uses 64-bit floating-point numbers (IEEE 754), which can represent values up to approximately 1.8 × 10³⁰⁸ and down to about 5 × 10⁻³²⁴. Beyond these limits, the number overflows to Infinity or underflows to 0. For exact integer representation, the limit is 2⁵³ (about 9 × 10¹⁵). The calculator handles all numbers within these ranges and shows results in scientific notation with up to 10 significant figures.

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Scientific Notation Calculator - Convert Numbers

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