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Scientific Notation & E-Notation Calculator

Q: What is the difference between scientific and engineering notation?

Scientific notation always has exactly one non-zero digit before the decimal point (1.23 × 10⁴), while engineering notation restricts exponents to multiples of 3 (12.3 × 10³), making it directly map to metric prefixes like kilo or milli.

Adds, subtracts, multiplies, divides, and raises numbers to powers in standard scientific notation and engineering notation, auto-formatting exponents and mapping SI metric prefixes from pico to tera.

Scientific & Engineering Notation Calculator

Perform high-precision operations on numbers in standard scientific (a × 10^b) and engineering format with SI prefixes

Presets:

Number 1 (a × 10^b)

× 10^

Number 2 (a × 10^b)

× 10^

Scientific Notation

1.2800 × 10^4

Engineering Notation

12.8000 × 10^3

Standard E-Notation

1.2800e+4

SI Metric Prefix

12.8000 kilo (k)

What is Scientific Notation?

Scientific notation expresses very large or very small real numbers in the standard normalized form a × 10^b, where 1 ≤ |a| < 10 and b is an integer exponent.

Engineering notation modifies this so that the exponent b is always an exact multiple of 3 (matching standard metric kilo, mega, micro, nano prefixes).

Formula & Step-by-Step Calculation

(a_1 \times 10^{b_1}) \times (a_2 \times 10^{b_2}) = (a_1 \times a_2) \times 10^{b_1 + b_2}

Multiplication sums exponents; division subtracts exponents; addition/subtraction normalizes to common powers of 10.

Worked Step-by-Step Examples

Example 1

Multiply (3.2 × 10^5) by (4.0 × 10^-2)

Solution: 1.28 × 10^4

• Multiply coefficients: 3.2 × 4.0 = 12.8

• Sum exponents: 10^(5 + (-2)) = 10^3

• Normalize to standard scientific form: 12.8 × 10^3 = 1.28 × 10^4

• Engineering notation: 12.8 × 10^3 (12.8 k)

Common Real-World & Academic Use Cases

✓ Astronomy celestial distances and light-year computations
✓ Quantum physics Planck scale and atomic radius math
✓ Electronic circuit component values (pF, nH, MΩ)
✓ Standardizing raw laboratory instrument output strings

How to Use the Scientific Notation & E-Notation Calculator

Input Number 1

Enter coefficient and exponent (e.g. 6.022 and 23 for Avogadro's number).

Choose Operator

Select Addition (+), Subtraction (-), Multiplication (×), or Division (÷).

Input Number 2 & Calculate

View results in Scientific Notation, Engineering Notation, E-notation, Real decimal, and SI prefix form.

Frequently Asked Questions

Q: What is the difference between scientific and engineering notation?

Scientific notation always has exactly one non-zero digit before the decimal point (1.23 × 10⁴), while engineering notation restricts exponents to multiples of 3 (12.3 × 10³), making it directly map to metric prefixes like kilo or milli.

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