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Scientific Notation Calculator

Powers of 10

1012
trillion
109
billion
106
million
103
thousand
100
one
10-3
milli
10-6
micro
10-9
nano

Quick Examples

299,792,458
= 2.998 × 10⁸
0.00000001
= 1 × 10⁻⁸
6.022 × 10²³
= Avogadro's number

Related Calculators

Exponent CalculatorLogarithm CalculatorSignificant Figures

Understanding Scientific Notation

What is Scientific Notation?

Scientific notation is a way to express very large or very small numbers in a compact form. It's written as a coefficient multiplied by a power of 10.

Standard Form

a × 10n
Where 1 ≤ |a| < 10 and n is an integer

Converting to Scientific Notation

Large Numbers

123,000,000
= 1.23 × 10⁸
(Move decimal 8 places left)

Small Numbers

0.00000456
= 4.56 × 10⁻⁶
(Move decimal 6 places right)

Operations with Scientific Notation

Multiplication

(a × 10m) × (b × 10n) = (a × b) × 10m+n
Multiply coefficients, add exponents

Division

(a × 10m) ÷ (b × 10n) = (a ÷ b) × 10m-n
Divide coefficients, subtract exponents

Addition/Subtraction

Make exponents equal first, then add/subtract coefficients
3.2 × 10⁴ + 5.0 × 10³ = 3.2 × 10⁴ + 0.5 × 10⁴ = 3.7 × 10⁴

Powers of 10 Reference

PowerPrefixSymbolName
10¹²teraTtrillion
10⁹gigaGbillion
10⁶megaMmillion
10³kilokthousand
10⁰one
10⁻³millimthousandth
10⁻⁶microμmillionth
10⁻⁹nanonbillionth
10⁻¹²picoptrillionth

Famous Numbers in Scientific Notation

Physical Constants

  • Speed of light: 2.998 × 10⁸ m/s
  • Avogadro's: 6.022 × 10²³
  • Planck's: 6.626 × 10⁻³⁴ J·s
  • Electron mass: 9.109 × 10⁻³¹ kg

Astronomical Distances

  • Earth-Sun: 1.496 × 10¹¹ m
  • Light year: 9.461 × 10¹⁵ m
  • Earth radius: 6.371 × 10⁶ m
  • Moon distance: 3.844 × 10⁸ m

E Notation

Calculators and programming languages often use "E notation" where 3.2E8 means 3.2 × 10⁸. The "E" stands for "exponent." This notation is commonly seen in scientific software and programming languages like Python, JavaScript, and Excel.

Frequently Asked Questions

How do you convert a number to scientific notation?

Move the decimal point until you have one non-zero digit before it (1-9). Count how many places you moved - this is your exponent. If you moved left (large number), exponent is positive. If moved right (small number), exponent is negative. Example: 45,000 = 4.5 x 10 to the 4.

How do you multiply numbers in scientific notation?

Multiply the coefficients (the numbers in front) and add the exponents. Example: (3 x 10 to the 4) x (2 x 10 to the 5) = (3 x 2) x 10 to the (4+5) = 6 x 10 to the 9. If the coefficient becomes 10 or more, adjust by increasing the exponent.

What does E notation mean on a calculator?

E notation is shorthand for scientific notation on calculators and computers. 3.2E8 means 3.2 x 10 to the 8 (320,000,000). E-5 means 10 to the negative 5. This format is used because superscripts are hard to type on keyboards.

How do you add numbers in scientific notation?

First, make the exponents the same by adjusting one number. Then add the coefficients and keep the common exponent. Example: 3.2 x 10 to the 4 + 5.0 x 10 to the 3 = 3.2 x 10 to the 4 + 0.5 x 10 to the 4 = 3.7 x 10 to the 4.