How do you simplify and write #(3.26times10^-6)(8.2times10^-6)# in standard form?
First, recognize that the expression involves the multiplication of four terms. Because of this, the parentheses can be removed.
Next, use the commutative property of multiplication to group the terms that are base 10 and the terms that are not base 10.
When terms containing like bases are multiplied together, their exponents will be added together. Mathematically, this is shown as:
Using this, the base-10 terms can be simplified:
Simplifying, we obtain:
However, in the standard form of scientific notation, the number preceding the base-10 term should always be between 1 and 10. To do this, move the decimal of the 26.732 term to the left by one place, and increase the exponent of the
Finally, since the number with the smallest number of significant figures was 8.2 in the original multiplication, the final answer should have 2 significant figures as well. Hence,