How do you write 1092 in scientific notation?

1 Answer
Sep 22, 2015

Answer:

#1.092xx10^3#

Explanation:

Scientific notation has two parts: a coefficient and an exponent. A number in sci. not. is written like this: #axx10^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 #axx10^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 -> 109.2 -> 10.92 -> 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 #1.092xx10^3#. If you were to actually perform this multiplication, you would get 1092 - which is what we want.