Scientific Notation Calculator - Convert to a × 10^n

A scientific notation calculator rewrites a number as a coefficient times a power of ten: a × 10ⁿ, where the coefficient a satisfies 1 ≤ |a| < 10 and n is an integer. The same idea is called standard form in many school systems outside the United States.

The point of the notation is scale. Avogadro’s number (about 602,214,076,000,000,000,000,000) and the mass of an electron (about 0.0000000000000000000000000000009109 kg) are painful to copy by hand and easy to mistype. Scientific notation keeps the significant digits in the coefficient and parks the magnitude in the exponent, which is what lab reports, physics homework, and spreadsheet E-notation all expect.

This free online scientific notation tool runs entirely in your browser. Nothing is uploaded. You can paste a plain decimal, E-notation such as 6.02e23, or a written form such as 6.02 × 10^23. The calculator normalizes the coefficient, reports the exponent, and can expand the value back to a standard decimal when the digit count is printable.

Using this standard form converter is straightforward:

1. Enter a number in the input field. Accepted forms include 6500, 0.0042, 6.5e3, 6.5E+3, 6.5x10^3, and 6.5 × 10^3.
2. Choose what to show: normalized scientific notation, a standard decimal, or engineering notation (exponent a multiple of 3).
3. Read the coefficient and exponent in the result panel. The tool also shows how many decimal places were moved and in which direction when you started from a plain decimal.
4. Copy the result, or clear the field to start over. The last input is saved locally in your browser for up to 30 days.

Note: exponents are limited to ±9999. A standard expansion longer than 80 digits is shown in E-notation instead of a wall of zeros.

To convert a decimal by hand:

1. Place the decimal so there is one non-zero digit to its left.
2. That new number is the coefficient a.
3. Count how many places the decimal moved. That count is |n|.
4. If you moved the decimal left, n is positive. If you moved it right, n is negative.

Example - 6,500:

• Move the decimal three places left: 6.500
• Coefficient a = 6.5 (trailing zeros after the point can drop if they are not significant in your assignment)
• 6.5 × 10³

Example - 0.0042:

• Move the decimal three places right: 4.2
• n = −3 because the original number is smaller than 1
• 4.2 × 10⁻³

Example - already in E-notation, 6.02e23:

• Coefficient 6.02, exponent 23
• Already normalized: 6.02 × 10²³

47,000 is 4.7 × 10⁴ in scientific notation and 47 × 10³ in engineering notation. The engineering exponent 3 matches the kilo- prefix: 47 × 10³ is 47 k in SI-ish shorthand. This calculator reports both so you can match whichever form your assignment or datasheet uses.

Scientific notation makes significant figures visible: in 4.20 × 10⁻³ the trailing zero is a significant digit. In the decimal 0.0042 it is harder to tell whether the measurement had two or three digits. This calculator keeps the digits you typed in the coefficient; it does not invent extra significant figures, and it does not apply a course’s rounding rule. If your teacher wants three significant figures, round the coefficient after you convert.

Multiplying in scientific notation: multiply coefficients and add exponents, then renormalize. (2.0 × 10³) × (4.0 × 10⁴) = 8.0 × 10⁷. Dividing: divide coefficients and subtract exponents. Adding is only valid after both numbers share the same exponent.