Scientific Notation Calculator

Convert numbers to and from scientific notation and perform arithmetic operations on numbers in scientific form.

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Scientific notation calculator: convert and compute in scientific form

A scientific notation calculator converts numbers to and from scientific notation and performs arithmetic operations on numbers in scientific form. Scientific notation is the standard way to write very large or very small numbers concisely, using a coefficient between 1 and 10 multiplied by a power of 10.

How scientific notation works

A number in scientific notation has the form a x 10^n, where a is between 1 and 10 and n is an integer. To convert a large number, move the decimal point left until only one non-zero digit remains before it, and count the positions moved: 93,000,000 becomes 9.3 x 10^7. For small numbers, move the decimal right and use a negative exponent: 0.00042 becomes 4.2 x 10^-4.

Multiplication in scientific notation multiplies the coefficients and adds the exponents: (3 x 10^4) x (2 x 10^3) = 6 x 10^7. Division divides the coefficients and subtracts the exponents.

a x 10^n (where 1 <= a < 10)

Standard scientific notation: a coefficient between 1 and 10 multiplied by a power of 10.

Where scientific notation is used

Physics and chemistry routinely deal with quantities spanning many orders of magnitude. The speed of light is approximately 3 x 10^8 m/s, the mass of a proton is about 1.67 x 10^-27 kg. Scientific notation makes these values readable and comparable.

Engineering, astronomy, and microbiology all rely on scientific notation for the same reason: it compresses very large or very small numbers into a compact, standard form that makes order-of-magnitude comparisons immediate.

Frequently asked questions

How do I add numbers in scientific notation?

Convert both numbers to the same power of 10, add the coefficients, and normalise if needed. For example, 3.0 x 10^4 + 5.0 x 10^3 = 3.0 x 10^4 + 0.5 x 10^4 = 3.5 x 10^4.

What is the difference between scientific and engineering notation?

Engineering notation restricts the exponent to multiples of 3, matching metric prefixes like kilo, mega, and micro. Scientific notation allows any integer exponent.

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