# How do you write 1092 in scientific notation?

Sep 22, 2015

$1.092 \times {10}^{3}$

#### Explanation:

Scientific notation has two parts: a coefficient and an exponent. A number in sci. not. is written like this: $a \times {10}^{b}$, where b is the exponent and a is the coefficient.

There are a few rules here: a has to be greater than one and less than ten, or greater than -10 and less than -1 ($1 < a < 10$, $- 10 < a < - 1$), and b has to be an integer (any non-fraction negative or positive number, like -2, 5, 3, -8, etc). So in other words, a has to be between 1 and 10 or -1 and -10, and b can't be a fraction.

For our example, we want to transform 1092 to $a \times {10}^{b}$. First we begin by making 1092 our $a$, and in the process we will find our $b$. Now, how to get 1092 in between 1 and 10? Divide by 1000, of course! Since dividing by 1000 is the same as moving the decimal point over to the left 3 times, we get $1092.0 \to 109.2 \to 10.92 \to 1.092$. Perfect - our $a$ is now 1.092, which is between 1 and 10.

We've also found our $b$. In order to get back to 1092, we have to multiply by 1000, which is the same as multiplying by 10^3. Hm...looks similar to ${10}^{b}$, right? That's because $b = 3$!

Putting it all together, $a$ = 1.092 and $b$ = 3, so 1092 in scientific notation is $1.092 \times {10}^{3}$. If you were to actually perform this multiplication, you would get 1092 - which is what we want.