How do you simplify #(8.39 xx 10^-7)(4.53 xx 10^9)#?
Consider the product of
Exactly the same happens when you are multiplying numbers in scientific notation.
See a solution process below:
First, rewrite the expression as:
Now, we can use this rule for exponents to simplify the 10s terms:
To write this in scientific notation we need to move the decimal point one place to the left so we need to add
Or, in standard terms:
By first combining the exponential terms, you can simplify the problem significantly, and get
The first thing to do is rewrite the function so all of the multiplication is outside of parentheses, and the exponents are grouped together:
Next, lets multiply the constants together, and use scientific notation to describe the result:
Re-writing the equation:
Finally, we combine the notation terms. When you multiply two exponential numbers with the same base, it is the same as adding the exponents together, like so:
using that principle:
Now, lets re-write the equation one last time with all of our simplification:
Suppose the idea of decimals is giving you a problem.
this is the same as
So we have:
Using the same argument as above we have:
So in Scientific notation we have: