# How would 0.073 be written in scientific notation?

Apr 22, 2016

0.073 would be written as $7.3 \cdot {10}^{-} 2$

#### Explanation:

Scientific notation uses multiplication or division of a number by 10s to express a number without taking up too much space.

For example we express large numbers like this:

$3000000000 = 3 \cdot {10}^{8}$

The number above, 300 million, is simply the same as taking 3 and multiplying it by 10 8 times. This is exactly what $\cdot {10}^{8}$ means. We can interpret the equation above as:

$300000000 = 3 \times 10 \cdot 10 \cdot 10 \cdot 10 \cdot 10 \cdot 10 \cdot 10 \cdot 10$

On the other hand, we can express very small numbers by dividing by ten, as in your example. We tell others that we are dividing by ten by using a negative exponent.

For example:

$3 \cdot {10}^{2} = 3 \cdot 10 \cdot 10$

While

$3 \cdot {10}^{-} 2 = \frac{3}{10 \cdot 10}$

There are some easy tricks to switch numbers between standard and scientific notation. For examples, check out this video: