Scientific Notation Calculator

Convert any number to scientific notation (a × 10n) with step-by-step explanation showing coefficient and exponent.

Enter a Number

Result

Scientific Notation
4.56 × 10^7
a × 10^n form
Coefficient (a) 4.56
Exponent (n) 7
Standard Form 45600000
E-Notation 4.56e7
Decimal Moved 7 places left

Step-by-Step Solution

45600000 = 4.56 × 10^7

What Is Scientific Notation?

Scientific notation is a way of expressing very large or very small numbers in a compact form. A number in scientific notation is written as a × 10n, where the coefficient a is a number with exactly one non-zero digit to the left of the decimal point (1 ≤ |a| < 10), and n is an integer exponent.

How to Convert to Scientific Notation

  1. Move the decimal point so that only one non-zero digit remains to its left.
  2. Count the number of places you moved the decimal point — this becomes the exponent n.
  3. If you moved the decimal to the left, the exponent is positive.
  4. If you moved the decimal to the right, the exponent is negative.

Examples

Large Number

Speed of light: 300,000,000 m/s

3 × 10^8

Small Number

Diameter of an atom: 0.0000000001 m

1 × 10^(-10)

Negative Number

Electron charge: -0.00000000016 C

-1.6 × 10^(-10)

Number Between 1 and 10

The number 5.5 is already in range

5.5 × 10^0

Avogadro's Number

602,200,000,000,000,000,000,000

6.022 × 10^23

Planck's Constant

0.0000000000000000000000000000000006626

6.626 × 10^(-34)

Applications of Scientific Notation

  • Physics: Expressing physical constants, distances, and measurements at extreme scales.
  • Chemistry: Avogadro's number, molar masses, atomic and molecular dimensions.
  • Astronomy: Distances between stars, galaxies, and other celestial objects.
  • Engineering: Electrical values (picofarads, megaohms), signal frequencies.
  • Biology: Cell sizes, microorganism counts, DNA base pair lengths.

E-Notation

In many calculators and programming languages, scientific notation is written using E-notation. For example, 4.56 × 107 is written as 4.56e7 or 4.56E7. The "e" stands for "exponent" and indicates the power of 10.

Rules to Remember

  • The coefficient must be between 1 and 10 (inclusive of 1, exclusive of 10).
  • A positive exponent means the original number is large (greater than or equal to 10).
  • A negative exponent means the original number is small (between 0 and 1).
  • An exponent of 0 means the number is already between 1 and 10.
  • Zero in scientific notation is simply 0 × 100.