Scientific Notation Converter

Move the decimal point so that exactly one non-zero digit sits to its left.

The number of places you moved gives the exponent — positive if you moved left, negative if you moved right.

Example: 0.00045 becomes 4.5 × 10⁻⁴.

Engineering notation uses exponents that are multiples of three, matching SI prefixes:

• kilo (10³)
• mega (10⁶)
• milli (10⁻³)
• micro (10⁻⁶)
• nano (10⁻⁹)

This makes it the preferred form in electronics and physics.

Scientific notation writes any nonzero number as a mantissa multiplied by an integer power of ten, in the form m × 10ⁿ where 1 ≤ |m| < 10. It compresses very large or very small values into a compact, comparable format.

According to Wolfram MathWorld, this standard form uniquely fixes the mantissa and exponent for every nonzero real number. For example, the speed of light is roughly 3 × 10⁸ metres per second, and a hydrogen atom's radius is about 5.3 × 10⁻¹¹ metres.

The power of ten records how many places the decimal point shifts, so you never have to write long strings of zeros to keep track of magnitude.

The formula is value = m × 10ⁿ, where m is the mantissa and n is the exponent. To convert, shift the decimal point until one nonzero digit remains on its left, then count the shifts: moving left makes n positive, moving right makes n negative.

As Khan Academy explains, 45,000 becomes 4.5 × 10⁴ (four places left) and 0.0032 becomes 3.2 × 10⁻³ (three places right). To reverse the process, multiply the mantissa by 10ⁿ, which simply relocates the decimal point n places.

This method scales cleanly across dozens of orders of magnitude without introducing rounding beyond your chosen significant figures.

To convert scientific notation back to a plain decimal, move the decimal point by the number of places given in the exponent: right for a positive exponent, left for a negative one.

For instance, 6.022 × 10²³ (the Avogadro constant, per NIST) expands to 602,200,000,000,000,000,000,000, while 4.5 × 10⁻⁴ becomes 0.00045. Fill any empty places with zeros.

Encyclopaedia Britannica notes this reversibility is what makes the notation practical: you compress for readability, then expand only when a full decimal is needed. Our converter shows the decimal form alongside every other representation so you can verify the placement instantly.

Standard form is the British and Commonwealth name for scientific notation, taught across UK, Australian, and Canadian curricula. It expresses a number as a × 10ⁿ where 1 ≤ a < 10 and n is an integer — identical rules to scientific notation.

So 8,300 in standard form is 8.3 × 10³, and 0.00067 is 6.7 × 10⁻⁴. Encyclopaedia Britannica and Khan Academy both treat the two terms as synonyms.

If a worksheet asks you to "write in standard form," apply exactly the same steps this converter uses for scientific notation; the answer will match precisely.

E-notation is a keyboard-friendly form used by calculators, spreadsheets, and programming languages, where the letter e (or E) replaces "× 10 to the power of."

So 4.5e-4 means 4.5 × 10⁻⁴ = 0.00045, and 6.022e23 means 6.022 × 10²³. The digits after e are the exponent, and a minus sign marks a negative power.

Because floating-point numbers in languages like Python, JavaScript, and C follow this convention, E-notation is essential when reading program output or scientific data files. Note that e here is the exponent marker, not Euler's number (≈ 2.71828); the two are unrelated despite sharing a letter.

Every digit in the mantissa of a properly written scientific-notation number is significant, which is why the notation removes ambiguity. In 4.5 × 10⁻⁴ there are two significant figures; in 6.022 × 10²³ there are four. The power of ten itself never counts.

This matters because a plain decimal like 1200 is ambiguous — it could carry two, three, or four significant figures — but 1.2 × 10³ unambiguously carries two and 1.200 × 10³ carries four.

Khan Academy stresses that leading zeros (as in 0.00045) are never significant; they only position the decimal point. Our tool reports the significant-figure count automatically for any input.

The order of magnitude is the exponent when a number is written in scientific notation — it tells you roughly how big or small the value is in powers of ten.

So 0.00045 = 4.5 × 10⁻⁴ has order of magnitude −4, while 123,456 = 1.23456 × 10⁵ has order of magnitude 5. Wolfram MathWorld describes the order of magnitude as the power of ten nearest a quantity, letting scientists compare vastly different scales at a glance.

Two numbers differing by one order of magnitude differ by a factor of ten. This concept underpins log scales like the Richter and decibel scales.

Scientific notation is indispensable wherever quantities span many powers of ten.

• Chemists use it for the Avogadro constant, 6.022 × 10²³ particles per mole (NIST).
• Physicists write the electron mass as about 9.109 × 10⁻³¹ kilograms and the elementary charge as roughly 1.602 × 10⁻¹⁹ coulombs.
• Astronomers express interstellar distances in metres, and computer engineers describe storage and clock speeds with the SI-aligned exponents of engineering notation.

It also simplifies calculation: multiplying powers of ten just means adding exponents. Encyclopaedia Britannica notes the notation became standard precisely because it keeps such extreme figures readable and error-resistant.

Several errors crop up repeatedly when writing scientific notation:

• The most frequent error is a mantissa outside the 1 ≤ |m| < 10 range: 45 × 10³ is not proper scientific notation because 45 exceeds 10 — it should be 4.5 × 10⁴.
• Another common slip is reversing the exponent sign; moving the decimal right (for small numbers like 0.00045) gives a negative exponent, not a positive one.
• Watch also for confusing engineering notation (exponents in multiples of three) with scientific notation, and for miscounting significant figures by including the power of ten.
• Finally, dropping trailing zeros that convey precision — writing 1.2 × 10³ when the data justifies 1.200 × 10³ — silently discards significant figures.