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MATH CALCULATOR

Scientific Notation Calculator

Express a number as a normalized coefficient times a power of ten. Compare scientific, engineering, and ordinary decimal forms of the same rounded value.

Calculator

For an ordinary decimal number, leave the power of ten at zero.
Integer exponent; negative values divide by powers of ten.
Controls rounding of all three representations.
YOUR RESULTS
Scientific notation1.2345 × 10^4
Engineering notation
12.345 × 10^3
Decimal form
12345
Normalized exponent
4

Understanding your result

Scientific notation keeps the nonzero coefficient’s absolute value at least one and below ten. Engineering notation uses an exponent divisible by three. Trailing zero padding is omitted, so the display does not assert measurement precision.

To compare two quantities as a simplified ratio, use the Ratio Calculator .

The formula

Value = entered coefficient × 10^entered power. Scientific form = a × 10^n, where 1 ≤ |a| < 10 for a nonzero value.

The significant-digit setting rounds the value first. Normalization then finds the exponent appropriate to the rounded number, including carry across a power-of-ten boundary. Zero is displayed with exponent zero by convention.

Worked example

With coefficient 12,345, power 0, and six significant digits, scientific form is 1.2345 × 10^4 and engineering form is 12.345 × 10^3. If 999.9 is rounded to three significant digits, it becomes 1 × 10^3 rather than 9.999 × 10^2.

How to use this calculator

  1. Enter an ordinary number as the coefficient, or supply the coefficient of an existing expression.
  2. Set the power of ten; use zero for an ordinary number.
  3. Choose significant digits and compare the three resulting forms.

Negative exponents and negative numbers

A negative exponent makes a quantity smaller by dividing by a power of ten. A negative coefficient determines the sign of the number. Those are independent choices: −2 × 10^-3 equals −0.002. The exponent field accepts whole numbers because this tool normalizes decimal powers rather than evaluating arbitrary exponential expressions.

Rounding and measurement precision

Significant digits count from the first nonzero digit, unlike decimal places, which count after the decimal point. Rounding can move a value into another exponent range. This calculator removes unnecessary trailing zeros and is intended for numerical conversion, not for preserving a laboratory record’s uncertainty notation. Inputs are limited to twelve reliable significant digits in the result; do not use it as an arbitrary-precision data archive.

Assumptions & limitations

What this calculation assumes

  • The input denotes a finite coefficient multiplied by an integer power of ten.

What to keep in mind

  • Does not add or multiply two scientific expressions or preserve significant trailing zeros.

Common questions

Why is engineering notation different?

Its exponent is a multiple of three, so its nonzero coefficient can range from one up to, but not including, one thousand.

Can I enter an ordinary small decimal?

Yes. Enter it as the coefficient and leave power at zero. For extremely small values, coefficient and exponent fields avoid typing a long sequence of zeros.

Sources & further reading