How do I convert a number to scientific notation?

Move the decimal point until you have a number between 1 and 10. Count how many places you moved it — that becomes the exponent. If you moved the decimal left, the exponent is positive; if right, it's negative. Example: 0.00045 → move decimal 4 places right → 4.5 × 10^-4.

How do I multiply numbers in scientific notation?

Multiply the coefficients together, then add the exponents. For example: (2.5 × 10^3) × (4.0 × 10^5) = (2.5 × 4.0) × 10^(3+5) = 10.0 × 10^8. Since 10.0 is not between 1 and 10, normalize to 1.0 × 10^9.

How do I add or subtract numbers in scientific notation?

First, rewrite both numbers with the same exponent (use the larger one). Then add or subtract the coefficients. Finally, normalize the result. Example: 3.2 × 10^4 + 5.0 × 10^3 → 3.2 × 10^4 + 0.5 × 10^4 = 3.7 × 10^4.

What is the difference between scientific and engineering notation?

Engineering notation is a variant where the exponent is always a multiple of 3 (e.g., 10^3, 10^6, 10^9). This maps directly to SI prefixes like kilo, mega, and giga. For example, 4.7 × 10^5 in scientific notation becomes 470 × 10^3 (470 kilo) in engineering notation.

How many significant figures does a scientific notation number have?

In scientific notation, all digits in the coefficient are significant. For example, 6.022 × 10^23 has 4 significant figures, while 3.0 × 10^8 has 2 significant figures. This is one of the key advantages of scientific notation — it makes the number of significant figures unambiguous.

Scientific Notation Calculator

Number

Decimal, E-notation (3.45e5), or a × 10^n format. Precision: up to 15 significant digits.

Scientific Notation

2.99792458 × 10⁸

All Formats

Your number expressed in every notation style

Scientific Notation

2.99792458 × 10⁸

a × 10ⁿ format

E-Notation

2.99792458e+8

Computer-friendly format

Engineering Notation

299.792458 × 10⁶

SI prefix: mega

Decimal Form

299792458

Standard number

Word Form

299.8 million

Human-readable scale

Order of Magnitude

10⁸

Power of 10 approximation

Step-by-Step Conversion

How the number was converted

1
Input value
299792458
2
Move decimal left
Move 8 places left to get 2.99792458
3
Exponent
10 raised to 8
4
Result
2.99792458 × 10⁸

What Is Scientific Notation?

The universal shorthand for extreme numbers used in science, engineering, and computing

Scientific notation expresses any number as a × 10ⁿ, where the coefficient a satisfies 1 ≤ |a| < 10 and n is an integer exponent. It was developed to handle numbers that are too large or too small to write conveniently in decimal form — from the distance between galaxies to the mass of subatomic particles.

a × 10ⁿ where 1 ≤ |a| < 10

Four rules govern the format:

The coefficient must be at least 1 and less than 10 (or exactly zero)
A positive exponent means the number is ≥ 10 — the decimal was shifted left
A negative exponent means the number is between 0 and 1 — the decimal was shifted right
An exponent of zero means the number is already between 1 and 10

How to Convert a Number to Scientific Notation

A clear three-step process with worked examples

Move the decimal point

Shift the decimal until you have a number between 1 and 10. This becomes your coefficient.

Count the places moved

The number of places becomes the exponent. Left = positive, right = negative.

Write in a × 10ⁿ form

Combine the coefficient and exponent. Verify: coefficient must be ≥ 1 and < 10.

Worked examples:

345,000

Move decimal 5 places left → 3.45 × 10⁵

0.00067

Move decimal 4 places right → 6.7 × 10⁻⁴

Arithmetic in Scientific Notation

Formulas and rules for all four operations

Operation	Rule	Example
Multiply	Multiply coefficients, add exponents	(2×10³)×(3×10⁴) = 6×10⁷
Divide	Divide coefficients, subtract exponents	(9×10⁸)÷(3×10⁵) = 3×10³
Add	Align exponents first, then add coefficients	(3.2×10⁴)+(5×10³) = 3.7×10⁴
Subtract	Align exponents first, then subtract coefficients	(5×10⁴)−(2×10⁴) = 3×10⁴

Key rule: After every operation, normalize the result so the coefficient is between 1 and 10. For example, 12.5 × 10⁴ becomes 1.25 × 10⁵.

Scientific vs Engineering vs E-Notation

How the same number looks in each format

Decimal	Scientific	Engineering	E-Notation
299,792,458	2.998 × 10⁸	299.8 × 10⁶ (mega)	2.998e+8
0.000001602	1.602 × 10⁻⁶	1.602 × 10⁻⁶ (micro)	1.602e-6
93,000,000	9.3 × 10⁷	93 × 10⁶ (mega)	9.3e+7

Engineering notation restricts the exponent to multiples of 3, aligning with SI prefixes (kilo, mega, giga, milli, micro, nano). E-notation is the format used by programming languages and spreadsheets.

SI Prefix Quick Reference

The complete scale from yocto (10⁻²⁴) to yotta (10²⁴)

Prefix	Symbol	Factor	Example
tera	T	10¹²	1 TB = 10¹² bytes
giga	G	10⁹	1 GHz = 10⁹ Hz
mega	M	10⁶	1 MW = 10⁶ watts
kilo	k	10³	1 km = 10³ meters
milli	m	10⁻³	1 mm = 10⁻³ meters
micro	μ	10⁻⁶	1 μs = 10⁻⁶ seconds
nano	n	10⁻⁹	1 nm = 10⁻⁹ meters
pico	p	10⁻¹²	1 pF = 10⁻¹² farads

Where Is Scientific Notation Used?

Real-world fields that rely on scientific notation every day

Physics & Chemistry

Avogadro's number (6.022 × 10²³), Planck's constant (6.626 × 10⁻³⁴ J·s), and electron charge (1.602 × 10⁻¹⁹ C) would be impossible to write without it.

Astronomy & Space

The distance to the nearest star is 4.0 × 10¹³ km. The observable universe is about 8.8 × 10²⁶ meters across — numbers that only make sense in scientific notation.

Biology & Medicine

A human body contains approximately 3.7 × 10¹³ cells. Bacteria are measured at 10⁻⁶ meters and viruses at 10⁻⁸ meters.

Computing & Data

Programming languages use E-notation (1.5e+8) for floating-point numbers. Storage is measured in terabytes (10¹²), and transistors operate at nanometer (10⁻⁹) scale.

Common Mistakes & Pro Tips

Avoid these pitfalls and learn expert shortcuts

Common Mistakes

Wrong coefficient range: 34.5 × 10⁴ is not valid — the coefficient must be < 10. Correct: 3.45 × 10⁵.

Exponent sign error: Decimal left = positive exponent. Decimal right = negative. Mixing these up is the #1 student mistake.

Forgetting to normalize: After arithmetic, always check the coefficient is between 1 and 10.

Pro Tips

Quick magnitude check: The exponent tells you the order of magnitude. 10⁶ = millions, 10⁹ = billions, 10¹² = trillions.

E-notation shortcut: 3.45e5 is not Euler's number — it means 3.45 × 10⁵. Most spreadsheets and languages use this format.

Sig figs clarity: In scientific notation, all digits in the coefficient are significant. 3.0 × 10⁸ has exactly 2 sig figs — no ambiguity.

Precision limit: This calculator uses IEEE-754 double-precision arithmetic, accurate to approximately 15 significant digits. Numbers beyond this range (e.g., 25+ digit integers) will be rounded.

Frequently Asked Questions

Common questions and detailed answers

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Last updated Apr 5, 2026