All HiSET: Math Resources
Example Questions
Example Question #1 : Solve Problems Using Scientific Notation
Simplify the following expression using scientific notation.
You can solve this problem in several ways. One way is to convert each number out of scientific notation and write it out fully, then find the sum of the two values and convert the answer back into scientific notation.
Another, potentially faster, way to solve this problem is to convert one answer into the same scientific-notational terms as the other and then sum them.
Example Question #1 : Solve Problems Using Scientific Notation
Multiply, and express the product in scientific notation:
Convert 7,200,000 to scientific notation as follows:
Move the (implied) decimal point until it is immediately after the first nonzero digit (the 7). This required moving the point six units to the left:
It follows that 7,200,000 can be rewritten as .
By similar reasoning, 5,000,000 can be rewritten as .
Thus,
Rearrange and regroup the expressions so that the powers of ten are together:
Multiply the numbers in front. Also, multiply the powers of ten by adding exponents:
In order for the number to be in scientific notation, the number in front must be between 1 and 10. An adjustment must be made by moving the implied decimal point in 36 one unit left. It follows that
Therefore,
,
the correct response.
Example Question #1 : Solve Problems Using Scientific Notation
Multiply:
Express the product in scientific notation.
None of the other choices gives the correct response.
Scientific notation refers to a number expressed in the form
,
where and
is an integer.
Each factor can be rewritten in scientific notation as follows:
Now, substitute:
Apply the Product of Powers Property:
This is in scientific notation and is the correct choice.
All HiSET: Math Resources
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