Final answer:
An order of magnitude represents the power of 10 nearest to a number in scientific notation. It is useful for making quick estimations for comparisons or calculations when precision is not essential.
Step-by-step explanation:
An order of magnitude is the power of 10 that most closely approximates the size of a number when it's expressed in scientific notation. For instance, the number 800 has an order of magnitude of 10³ since 800 is closest to the power of 10 that is 1,000. If we express the number 800 in scientific notation, it would be 8 x 10², indicating that its order of magnitude is 10².
Estimates based on order of magnitude are quite useful despite their potential to be off by a factor of up to 10 times larger or smaller. They facilitate quick and easy comparisons or calculations when exact precision is not necessary.
For example, understanding that the diameter of an atom is on the order of 10⁻¹⁰ m and the diameter of the Sun is on the order of 10⁹ m gives us a helpful visualization of scale without needing to use exact sizes.
The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a different order of magnitude. All quantities that can be expressed as a product of a specific power of 10 are said to be of the same order of magnitude.
For example, the number 800 can be written as 8x10², and the number 450 can be written as 4.5×10². Thus, the numbers 800 and 450 are of the same order of magnitude: 10². Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of 10-9 m, while the diameter of the Sun is on the order of 109 m.