How to Use Scientific Notation

HOW-TO GUIDES

How to use scientific notation

Scientific notation writes a number as a value between 1 and 10 times a power of ten, keeping very large and very small numbers compact. This guide shows how to convert numbers and how to multiply and divide them.

What scientific notation is

A number is written as a value between 1 and 10 times a power of ten, so 384,400 becomes 3.844 times ten to the fifth. The first part is called the mantissa; the exponent records the scale. This keeps long strings of zeros manageable.

Converting a number

  1. Move the decimal point so one nonzero digit stays in front of it.
  2. Count how many places you moved it.
  3. That count is the exponent: positive if you moved left, negative if you moved right.
  4. Write the result as the leading number times ten to that power.
Example
0.00045 becomes 4.5 × 10⁻⁴; the decimal moved 4 places right, so the exponent is negative 4.

Multiplying and dividing

Scientific notation makes these operations easy. To multiply, multiply the leading numbers and add the exponents. To divide, divide the leading numbers and subtract the exponents. If the leading result falls outside the range 1 to 10, adjust the exponent to put it back in range.

Example
(2 × 10³) × (3 × 10⁴) = 6 × 10⁷.
Key takeaways

  • Scientific notation is a number from 1 to 10 times a power of ten.
  • Move the decimal to leave one digit in front; the moves set the exponent.
  • Moving left gives a positive exponent; right gives negative.
  • Multiply by multiplying leading numbers and adding exponents.
  • Divide by dividing leading numbers and subtracting exponents.

Handy references

See the Scientific Notation Chart and the Powers of Ten Chart.

FAQ

How do I write a number in scientific notation?

Express it as a number between 1 and 10 times a power of ten, with the exponent equal to how many places the decimal moved.

What does a negative exponent mean here?

A number smaller than one. 10 to the negative 3 is 0.001.

How do I multiply numbers in scientific notation?

Multiply the leading numbers and add the exponents, then adjust so the leading number is between 1 and 10.

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