# Order of magnitude

The order of magnitude of a number is the power of 10 that the number is closest to. For example, the order of magnitude of 1234 is 3, because 1234 is closest to 1000 (10^3).

The order of magnitude can be used to estimate the size of a number. For example, if someone says that the population of a city is about "a hundred thousand", this is an estimate of the city's population to within one order of magnitude. How do you calculate the order of magnitude? In mathematics, the order of magnitude of a number is the logarithm of the absolute value of the number. For example, the order of magnitude of 100 is 2, because the logarithm of 100 (2) is two.

### What is an order of magnitude example?

An order of magnitude is a factor of ten.

For example, the mass of the Sun is about 333,000 times the mass of the Earth. So the Sun's mass is 3.33 x 10^5 kg and the Earth's mass is 3.33 x 10^3 kg.

The Sun is about a million times brighter than the Earth. So the Sun's luminosity is 3.86 x 10^6 W and the Earth's luminosity is 3.86 x 10^3 W. How many orders of magnitude is 1000? There are three orders of magnitude between 1000 and 1.

#### What is the order of magnitude of 8?

The order of magnitude of a number is the power of 10 that the number is closest to. In other words, it is the number of zeroes in the number.

So, the order of magnitude of 8 is 1 because it is closest to 10 (1 zero). What is the order of magnitude of 2? The order of magnitude of 2 is 10.