Scientific Notation Calculator

Enter any number to convert it to scientific notation (E notation) and see the coefficient and exponent.

What Is Scientific Notation?

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Why Scientific Notation Matters

Scientific notation compresses extremely large or small numbers into a compact form: a × 10ⁿ, where 1 ≤ a < 10. The distance from Earth to the Sun is about 149,600,000 km — in scientific notation: 1.496 × 10⁸ km. The mass of a proton is 0.0000000000000000000000000016726 kg — written as 1.6726 × 10⁻²⁷ kg. This notation makes multiplication and division trivial: multiply the coefficients and add (or subtract) the exponents.

Fields that rely on scientific notation daily: astronomy, chemistry, physics, engineering, and finance (where national debts run into the trillions — 10¹²).

Converting Between Standard and Scientific Notation

To convert a standard number to scientific notation: move the decimal point until you have one non-zero digit to its left. Count how many places you moved — that is your exponent. Moving left gives a positive exponent; moving right gives a negative one.

Converting Between Scientific and Standard Notation

To convert a large number to scientific notation: move the decimal point left until one non-zero digit remains before it; the number of moves is the positive exponent. 93,000,000 → 9.3 × 10⁷ (moved 7 places left). To convert a small number: move right until one non-zero digit is before the decimal; count of moves is the negative exponent. 0.00045 → 4.5 × 10⁻⁴ (moved 4 places right). To convert back, move the decimal in the direction indicated by the exponent sign.

Scientific notation is used in astronomy (Sun's mass = 1.989 × 10³⁰ kg), chemistry (Avogadro's number = 6.022 × 10²³), physics (speed of light = 3 × 10⁸ m/s), and biology (a red blood cell diameter = 8 × 10⁻⁶ m). Computers store numbers in IEEE 754 floating-point format, which is binary scientific notation. When multiplying measurements in scientific notation, significant figures in the result cannot exceed those in the least precise measurement.

Scientific Notation Examples

Rules for Scientific Notation Operations

Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10, making very large or very small numbers easy to read and manipulate. When multiplying in scientific notation, multiply the coefficients and add the exponents: (3 times 10 squared) times (2 times 10 cubed) equals 6 times 10 to the fifth. When dividing, divide the coefficients and subtract the exponent of the divisor from that of the dividend. When adding or subtracting, first adjust both numbers to the same power of 10, then add or subtract the coefficients, and finally re-normalize if the result is not between 1 and 10. Significant figures in the coefficient determine measurement precision. Converting to and from standard notation requires moving the decimal point left (for large numbers, positive exponent) or right (for small numbers, negative exponent) by the number of positions equal to the absolute value of the exponent. Scientific notation is standard in chemistry (Avogadro's number: 6.022 times 10 to the 23rd), physics (speed of light: 3 times 10 to the 8th meters per second), and astronomy (distance to Andromeda: 2.537 times 10 to the 22nd meters).

Scientific Notation Reference Table