🧪 Math & Science

Scientific Notation Converter

Convert between standard, scientific, E-notation and engineering notation with metric prefix output and step-by-step explanation. Built-in calculator for ×, ÷, +, − and powers. Scientific constants included. Live as you type.

5 output formats simultaneously Engineering notation + metric prefix Step-by-step explanation Calculator with full working

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Enter any format: 123456789 · 1.23e8 · 1.23×10^8 · 45.6×10^3 (engineering)

Significant figures:

Standarddecimal

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Scientifica × 10ⁿ

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E-notationaen

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Engineeringexp ÷3

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Metric prefixkilo/mega…

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Order ofmagnitude

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📖 Step-by-step explanation ▼

Enter a number to see the steps.

Enter numbers in any format: standard, scientific (1.5e6), or ×10ⁿ notation.

Number A

Number B

Click any constant to copy its value to the converter.

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Features

Engineering notation + metric prefix — what every other free converter skips

Most scientific notation converters show you scientific and E-notation. This tool adds engineering notation (exponent always a multiple of 3), the metric prefix name, a full step-by-step explanation, a calculator with working, and quick-insert scientific constants.

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Engineering notation

Exponent is always a multiple of 3 (…−9, −6, −3, 0, 3, 6, 9…), so outputs align with metric SI prefixes. 45,000 becomes 45×10³ rather than 4.5×10⁴. Makes values readable as “45 kilo-” without a separate calculation. Absent on all major free tools.

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Metric prefix output

Automatically names the metric prefix: 3.2×10⁶ → “3.2 Mega”. Covers all 20 SI prefixes from quecto (10⁻³0) to quetta (10³0). Useful for electronics, physics and engineering when expressing component values (capacitance, resistance, frequency) in natural units.

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Step-by-step explanation

Click “Step-by-step explanation” to see how the conversion works: where the decimal point moved, how the exponent was determined, how the engineering exponent was rounded to a multiple of 3. Essential for students learning scientific notation for exams.

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Scientific notation calculator

Multiply, divide, add, subtract and raise to power using numbers in any notation format. Full step-by-step working shown — coefficient operations and exponent arithmetic displayed separately. Enter A, choose an operator, enter B, click Calculate.

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Scientific constants

Quick-insert 12 common constants — speed of light, Avogadro’s number, Planck’s constant, gravitational constant, electron mass, and more. Click any constant to load its value into the converter instantly.

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Universal input format

Enter numbers in any format: plain decimal (0.0000045), E-notation (4.5e-6), scientific with caret (4.5×10^-6), or engineering notation (4.5×10^-6). The parser auto-detects the format. Significant figures control from 2 to full precision.

How to use

How to convert scientific notation online

Enter your number in any format

Type a number directly (e.g. 299792458), in E-notation (2.998e8), or in scientific notation using a caret (2.998×10^8). All five output rows update instantly. Use the example buttons to load common values like the speed of light or Avogadro’s number immediately.

Choose significant figures

Select 2–10 significant figures or “Full precision” from the dropdown. The coefficient in scientific, E and engineering notation updates immediately. For most engineering work, 3–4 significant figures is standard.

Read the metric prefix (engineering row)

The highlighted Engineering row shows the notation with exponent rounded to the nearest multiple of 3. The Metric prefix row names the prefix: kilo, mega, giga, milli, micro, nano, pico, etc. These two rows are the key differentiator — absent on most free tools.

Expand step-by-step for learning

Click “Step-by-step explanation” to see exactly how the conversion works — decimal point movement, exponent calculation, and engineering exponent rounding. Use the Calculator tab to multiply, divide or add numbers in scientific notation with full working shown.

Quick reference

SI metric prefixes — engineering notation reference

Prefix	Symbol	Power	Multiplier	Example use
Quetta	Q	10³⁰	1,000,000,000,000,000,000,000,000,000,000	Cosmological data
Ronna	R	10²⁷	1,000,000,000,000,000,000,000,000,000	Cosmological data
Yotta	Y	10²⁴	1,000,000,000,000,000,000,000,000	Global internet traffic
Zetta	Z	10²¹	1,000,000,000,000,000,000,000	Global data storage
Exa	E	10¹⁸	1,000,000,000,000,000,000	Exabytes of data
Peta	P	10¹⁵	1,000,000,000,000,000	Petaflops of compute
Tera	T	10¹²	1,000,000,000,000	Terahertz frequencies
Giga	G	10⁹	1,000,000,000	GHz CPU speed
Mega	M	10⁶	1,000,000	MHz, megaohm
Kilo	k	10³	1,000	km, kg, kHz
(base)	—	10⁰	1	metres, grams
Milli	m	10⁻³	0.001	mm, mA, mV
Micro	μ	10⁻⁶	0.000001	μF, μm, μs
Nano	n	10⁻⁹	0.000000001	nm, nF, ns
Pico	p	10⁻¹²	0.000000000001	pF capacitors
Femto	f	10⁻¹⁵	0.000000000000001	Femtosecond lasers
Atto	a	10⁻¹⁸	0.000000000000000001	Attosecond pulses
Zepto	z	10⁻²¹	10⁻²¹	Particle physics
Yocto	y	10⁻²⁴	10⁻²⁴	Quark-scale physics

Complete guide

Scientific Notation — A Complete Guide to Conversion, Engineering Notation and Metric Prefixes

Scientific notation is the standard way to write very large and very small numbers in science and engineering. Instead of writing 299,792,458 (the speed of light in metres per second), scientists write 2.998×10⁸ — a coefficient between 1 and 10 multiplied by a power of ten. The format makes arithmetic easier, keeps significant figures explicit, and works across 60 orders of magnitude from the size of a quark to the observable universe.

Convert standard form to scientific notation online free

Converting a number to scientific notation follows a fixed algorithm. Step 1: move the decimal point until there is exactly one non-zero digit to its left — this becomes the coefficient. Step 2: count how many places the decimal moved — this is the exponent. If the decimal moved left (for large numbers), the exponent is positive. If it moved right (for small numbers), the exponent is negative. For example, 0.00000045 requires moving the decimal 7 places right, giving 4.5×10⁻⁷. This tool shows these steps explicitly in the “Step-by-step” section.

Scientific notation calculator with steps

Arithmetic in scientific notation follows rules that simplify dramatically compared to working with full numbers. Multiplication: multiply the coefficients and add the exponents — (3×10⁴) × (2×10³) = 6×10⁷. Division: divide the coefficients and subtract the exponents. Addition and subtraction: align the exponents first (rewrite both numbers to the same power of 10), then add or subtract the coefficients. Powers: raise the coefficient to the power and multiply the exponent. The Calculator tab in this tool shows all of these steps explicitly so you can follow the working and learn the method.

Engineering notation with metric prefixes converter

Engineering notation is a variation of scientific notation where the exponent is always a multiple of 3 — matching the SI metric prefix system. Where scientific notation gives 4.5×10⁴, engineering notation gives 45×10³, which can be read directly as “45 kilo-”. This matters enormously in electronics and electrical engineering: a capacitor value of 4.7×10⁻¹0 F would be written 4.7 pF (picofarads) in engineering notation. A resistance of 22,000Ω becomes 22kΩ. The metric prefix replaces the explicit power of ten, making component values and measurements immediately readable without mental arithmetic.

Standard form converter UK

In the United Kingdom, “standard form” refers to exactly what Americans call “scientific notation”: a number written as A × 10ⁿ where 1 ≤ A < 10 and n is an integer. The term appears in the UK GCSE Mathematics curriculum and the International Baccalaureate. This tool converts any number to and from standard form — enter a decimal number to get it in standard form, or enter a standard form expression (such as 3.6×10^5 or 3.6e5) to convert back to a decimal. The step-by-step section explains the conversion process in the same language used in GCSE coursework.

E notation to decimal converter

E-notation (or scientific E-notation) is the computer and calculator format for scientific notation. It replaces “× 10ⁿ” with “E” or “e” because programming languages and calculators cannot display superscripts. 3.56×10⁶ becomes 3.56E6 or 3.56e6. E-notation appears in Python, JavaScript, C, Java, Excel and most spreadsheet and data analysis tools when numbers get very large or very small. This tool accepts E-notation as input and converts it back to all formats simultaneously, including the standard decimal form.

Significant figures in scientific notation

Significant figures (sig figs) determine the precision of a measurement expressed in scientific notation. The coefficient in scientific notation makes the number of significant figures explicit: 3.00×10⁴ has three significant figures, while 3×10⁴ has one. This is a key advantage of scientific notation over standard decimal form — 30,000 could have one, two, three, four or five significant figures, but you cannot tell without context. This tool’s significant figures selector (2–10, or full precision) rounds the coefficient to the specified number of sig figs in all output rows.

Frequently asked questions

What is scientific notation?

Scientific notation expresses any number as a × 10ⁿ, where a is a coefficient between 1 and 10 (or −10 and −1 for negative numbers) and n is an integer exponent. For example, 5,400,000 = 5.4×10⁶. It simplifies working with very large numbers (e.g. the distance to a star in metres) and very small numbers (e.g. the mass of an electron in kg) by keeping the magnitude as the exponent rather than writing out all the zeros.

What is engineering notation and how is it different from scientific notation?

Both use a coefficient times a power of 10, but scientific notation requires the coefficient to be between 1 and 10, while engineering notation requires the exponent to be a multiple of 3. So 45,000 in scientific notation is 4.5×10⁴, but in engineering notation it is 45×10³ (because 10³ is the nearest multiple-of-3 exponent). This aligns with SI metric prefixes: 10³ = kilo, 10⁶ = mega, 10⁹ = giga, 10⁻³ = milli, 10⁻⁶ = micro.

What is E-notation?

E-notation is the computer-friendly version of scientific notation. It replaces “× 10ⁿ” with “e” (or “E”) because superscripts are not available in many programming contexts. 3.56×10⁶ becomes 3.56e6. E-notation is used in Python, JavaScript, C, Excel and most scientific calculators. It is identical in meaning to scientific notation — only the display format differs.

What is standard form (UK)?

In the UK, “standard form” means the same as “scientific notation” in the US — a number written as A × 10ⁿ where 1 ≤ A < 10. It is taught in the GCSE Mathematics curriculum. This tool’s “Scientific” output row is the standard form output. You can enter a number in any format and copy the standard form result directly for GCSE assignments or exam work.

How do I multiply numbers in scientific notation?

Multiply the coefficients and add the exponents: (a × 10˜) × (b × 10ⁱ) = (a×b) × 10ⁿ⁺ᵐ. If the resulting coefficient is not between 1 and 10, adjust it. Example: (3×10⁴) × (2×10³) = 6×10⁷. Use the Calculator tab in this tool to see full step-by-step working for any multiplication.

What is the order of magnitude?

The order of magnitude is the exponent n in scientific notation a×10ⁿ. It gives a rough sense of the scale of a number. For example, the mass of a proton (1.67×10⁻²⁷ kg) has order of magnitude −27, and the mass of the Sun (2×10³0 kg) has order of magnitude 30. Numbers that differ by one order of magnitude are 10 times apart. Numbers that differ by 3 orders of magnitude are 1,000 times apart.

How do I enter scientific notation in this converter?

You can enter numbers in any of these formats: a plain decimal number (0.000045), E-notation using “e” (4.5e-5), or scientific notation using a caret for the exponent (4.5×10^-5 or just 4.5^-5). The parser auto-detects the format. Negative exponents must use a minus sign (e.g. 4.5e-5, not 4.5e5-). For engineering notation input, enter the coefficient and exponent directly (e.g. 45×10^3).

What scientific constants are available?

The Constants tab includes 12 fundamental constants: speed of light in vacuum (c = 2.998×10⁸ m/s), Avogadro’s number (Nₐ = 6.022×10²³), Planck’s constant (h = 6.626×10⁻³⁴ J·s), gravitational constant (G = 6.674×10⁻¹¹ m³kg⁻¹s⁻²), elementary charge, Boltzmann constant, electron mass, proton mass, and others. Click any to load it into the converter.

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