Scientific Notation Calculator

Convert any number to scientific notation, E notation and engineering notation (or back to standard form), and add, subtract, multiply or divide numbers written in scientific notation, with each step shown.

Convert a number

Scientific notation
4.5600 × 10⁻⁵
E notation
4.5600e-5
Engineering
45.600 × 10⁻⁶
Standard form
0.000045600
Significant figures
5

How to convert

  1. Place the decimal point after the first non-zero digit to get a number between 1 and 104.5600
  2. Count how many places the point moved: 5 to the rightmoving right means a negative exponent: 10⁻⁵
  3. Write mantissa × 10 to that power4.5600 × 10⁻⁵

Calculate in scientific notation

Answer
1.280000000 × 10⁴
Rounded to 2 sig figs
1.3 × 10⁴

Step-by-step working

  1. Multiply the mantissas3.2 × 4 = 12.8
  2. Add the exponents10⁵ × 10⁻² = 10³
  3. Normalise so the mantissa is between 1 and 101.280000000 × 10⁴

Formula a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

Slide the decimal point

Scientific notation is just bookkeeping for “where is the decimal point?”. Keep the digits 6.02, move the exponent, and watch the point hop one place for each step. Positive exponents move it right (big numbers); negative exponents move it left (small numbers).

6.02 × 10²³

= 602,000,000,000,000,000,000,000

At 10²³ this is Avogadro’s number, about how many molecules are in 18 g of water (6.022 × 10²³ per mole, per the 2019 SI definition). Writing all those zeros is where mistakes creep in; the exponent carries the size so the mantissa can carry the precision.

How to convert to scientific notation

  1. Move the decimal point so exactly one non-zero digit is in front of it.
  2. Count the places you moved it.
  3. Moved left (a big number): the exponent is positive. Moved right (a small number): the exponent is negative.

45,600,000 → 4.56 × 10⁷. 0.00032 → 3.2 × 10⁻⁴. Keep only the significant digits in the mantissa: trailing zeros in 45,600,000 are placeholders unless you know they were measured.

Arithmetic in scientific notation

  • Multiply: multiply the mantissas, add the exponents. (3 × 10⁴)(2 × 10⁵) = 6 × 10⁹.
  • Divide: divide the mantissas, subtract the exponents.
  • Add/subtract: first rewrite both numbers with the same exponent, then add the mantissas.
  • Finally, renormalise so the mantissa is between 1 and 10.

For multiplication and division the calculator also rounds the answer to the correct number of significant figures.

Frequently asked questions

How do you write 6000 in scientific notation?

6 × 10³. Move the decimal point 3 places left to get a number between 1 and 10 (6), and the exponent is the number of places moved: 3. If the trailing zeros are measured (6000. or 6.000 × 10³), keep them in the mantissa.

How do you add numbers in scientific notation, like 5.3 × 10⁵ + 3.8 × 10⁴?

Rewrite one so the exponents match: 3.8 × 10⁴ = 0.38 × 10⁵. Then add the mantissas: (5.3 + 0.38) × 10⁵ = 5.68 × 10⁵. Use the arithmetic panel above to check.

How do I do scientific notation on a calculator?

Use the EE or EXP key (on a TI-84, 2nd then the comma key) to enter the “× 10^” part: 3.2 EE 5 means 3.2 × 10⁵. Results show as 3.2E5. Avoid typing × 10 ^ by hand, because order of operations can split it from the mantissa.

How do I convert scientific notation back to a normal number?

Move the decimal point right by the exponent if it is positive, left if it is negative, filling with zeros: 4.56 × 10⁷ = 45,600,000 and 7.21 × 10⁻⁵ = 0.0000721. Type either form above and the converter shows the other.

What is E notation?

Calculator and spreadsheet shorthand: 3.2E-4 means 3.2 × 10⁻⁴. You can type it into this calculator.

What is engineering notation?

Like scientific notation but the exponent is always a multiple of 3 (10³, 10⁻⁶), matching SI prefixes such as kilo, milli and micro. 45,600 is 45.6 × 10³.

Is 0.5 × 10³ in scientific notation?

Not in normalised form, because the mantissa must be at least 1. Write it as 5 × 10².