Standard Form / Scientific Notation

In physics, we often encounter numbers that are either very small or very large. For example, the width of the observable universe is approximately 880,000,000,000,000,000,000,000,000 meters (88 with 25 zeros). Using such large numbers frequently can be time-consuming and prone to error.

Scientific notation provides a convenient way to write very large or small numbers using powers of ten. This notation simplifies the representation and calculation with such numbers.

Scientific Notation

Scientific notation represents a number as the product of a mantissa (a number greater than 1 and less than 10) and a power of 10 (the exponent). The general form is:

number = mantissa × 10^exponent

For example:

  • The width of the observable universe can be written as 8.8 × 1026 meters, where '8.8' is the mantissa and '26' is the exponent.
  • The mass of Earth is 5,980,000,000,000,000,000,000,000 kg, which can be written as 5.98 × 1024 kg.
  • The diameter of a hydrogen nucleus is about 0.0000000000000017 meters, which can be written as 1.7 × 10-15 meters.