Scientific Notation Calculator

Scientific notation at a glance#

A scientific notation calculator rewrites a number as a × 10ⁿ, where a is at least 1 and less than 10 and n is a whole-number exponent. Move the decimal point until one non-zero digit sits in front of it, then count the moves: left gives a positive exponent, right gives a negative one. So 4500 becomes 4.5 × 10³ and 0.0023 becomes 2.3 × 10⁻³.

For 4500, the decimal moves 3 places left to sit after the 4, giving 4.5 and an exponent of 3: 4.5 × 10³ = 4.5 × 1000 = 4500. For 0.0023, the decimal moves 3 places right, giving 2.3 and an exponent of −3: 2.3 × 10⁻³ = 2.3 ÷ 1000 = 0.0023.

The same rule covers very large and very small numbers, so the Earth’s population of about 7.8 billion is 7.8 × 10⁹. Standard form is the same thing under another name. Enter your number in the calculator above for the exact scientific notation, e-notation or engineering-notation result, with the exponent and significant figures handled for you.

E-notation and engineering notation#

E-notation replaces "× 10" with the letter e, which is how calculators and code show the same value. So 2 × 10⁴ reads as 2e4, and 5.2 × 10⁻⁴ reads as 5.2e-4. The number is identical; only the symbol changes.

Engineering notation is scientific notation with the exponent locked to a multiple of 3, so it lines up with SI prefixes like kilo (10³), mega (10⁶) and milli (10⁻³). The coefficient can then run from 1 up to just under 1000. For example 47000 is 4.7 × 10⁴ in scientific notation but 47 × 10³ in engineering notation, which maps straight to 47 kilo-units.

Doing arithmetic in scientific notation#

To multiply, multiply the coefficients and add the exponents. (3 × 10⁴) × (2 × 10³) = 6 × 10⁷. To divide, divide the coefficients and subtract the exponents: (6 × 10⁵) ÷ (2 × 10²) = 3 × 10³.

To add or subtract, first match the exponents, then add the coefficients. (4 × 10³) + (5 × 10²) becomes (4 × 10³) + (0.5 × 10³) = 4.5 × 10³. If a result lands outside the 1-to-10 range for the coefficient, shift the decimal once more and adjust the exponent, so 12 × 10³ is rewritten as 1.2 × 10⁴.

Scientific notation FAQ#

What is the difference between scientific, e-notation and engineering notation?#

Scientific notation writes a number as a coefficient from 1 up to 10 times a power of 10. E-notation is the same value with e standing in for "× 10", so 2 × 10³ is 2e3. Engineering notation keeps the exponent a multiple of 3 to match SI prefixes, so 2 × 10⁴ becomes 20 × 10³.

How do you write a very small number in scientific notation?#

Move the decimal point right until one non-zero digit sits in front of it, then make the exponent negative and equal to the number of moves. So 0.00052 becomes 5.2 × 10⁻⁴, because the decimal moves 4 places right. A negative exponent always means the number is smaller than 1.

How do you multiply and divide numbers in scientific notation?#

For multiplication, multiply the coefficients and add the exponents. For division, divide the coefficients and subtract the exponents. Then renormalise so the coefficient stays between 1 and 10. For example (6 × 10⁵) ÷ (3 × 10²) = 2 × 10³.

How do you add and subtract numbers in scientific notation?#

Rewrite both numbers so they share the same exponent, then add or subtract the coefficients and keep that exponent. (7 × 10⁴) − (3 × 10³) becomes (7 × 10⁴) − (0.3 × 10⁴) = 6.7 × 10⁴.

Is standard form the same as scientific notation?#

Yes. Standard form is the term used in the UK and many other countries for what the US calls scientific notation. A number written one way is correct in the other, so 45000 is 4.5 × 10⁴ in both.