Scientific Notation Calculator

How to use the scientific notation calculator

1. Choose what to do. Convert one number, or add, subtract, multiply or divide two numbers.
2. Type your number in any form. Ordinary decimals (0.000045), whole numbers with or without commas (45,000), E notation (4.5e-5) and written powers (4.5 x 10^-5) all work.
3. Pick the significant figures (optional). Keep every digit, or round the answer to a set number of significant figures for a lab report or homework.
4. Read the results. You get the answer in scientific notation, E notation, standard decimal form and engineering notation, plus the exponent, the number of significant figures and the working for calculations.

The calculator works with up to about 15 significant digits, the precision of standard computer numbers.

What is scientific notation?

Scientific notation writes any number as a coefficient between 1 and 10 multiplied by a power of 10:

N = a × 10ⁿ, where 1 ≤ |a| < 10 and n is a whole number

It makes very large and very small numbers short and easy to compare. The speed of light, 299,792,458 m/s, becomes 2.99792458 × 10⁸, and the width of a human hair, about 0.00007 m, becomes 7 × 10⁻⁵.

How to convert to scientific notation

1. Move the decimal point until exactly one non-zero digit is left of it.
2. Count how many places you moved it. That count is the exponent.
3. If you moved the point left (a big number), the exponent is positive. If you moved it right (a small number), the exponent is negative.

Examples:

• 45,000 → 4.5 × 10⁴ (the point moved 4 places left)
• 0.00045 → 4.5 × 10⁻⁴ (the point moved 4 places right)

To convert back to standard form, move the decimal point the other way: right for a positive exponent, left for a negative one.

E notation and engineering notation

• E notation replaces "× 10^" with the letter e, so 4.5 × 10⁻⁴ becomes 4.5e-4. Calculators, spreadsheets and code use it.
• Engineering notation only uses exponents that are multiples of 3, which match metric prefixes such as kilo (10³), mega (10⁶) and milli (10⁻³). For example, 45,000 is 45 × 10³.

Calculating with scientific notation

• Multiply: multiply the coefficients and add the exponents. (3 × 10⁴) × (2 × 10³) = 6 × 10⁷.
• Divide: divide the coefficients and subtract the exponents. (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴.
• Add or subtract: rewrite both numbers with the same exponent first, then add or subtract the coefficients. 3 × 10⁴ + 5 × 10³ = 3 × 10⁴ + 0.5 × 10⁴ = 3.5 × 10⁴.

After any step, adjust the coefficient back to between 1 and 10 if needed, changing the exponent to match.