Approximating with powers of 10

The  exercise appears under the 8th grade (U.S.) Math Mission. This exercise introduces an application of orders of magnitude to finding estimated answers to applied word problems.

Types of Problems
There are two types of problems in this exercise:


 * 1) Use estimates to get close to a final answer: This problem has two initial quantities and asks for the answer to a question involving both these quantities. The student is expected to find good estimates of both the initial amounts, and the correct answer to the problem based on those estimates.Awoom1.png
 * 2) Find the final estimate: This problem also provides some initial information and asks a questions that uses this information. Here the student is only expected to find a final estimate and select the answer from a multiple choice list.Awoom2.png

Strategies
Knowledge of estimation, multiplication/division, and exponents rules are encouraged to ensure success on this exercise.
 * 1) The numbers work out nicely in the calculations, so a calculator should be unnecessary and may even be a hindrance.
 * 2) Since only approximations are required, exact answers can take additional work and are not needed.
 * 3) When multiplying exponential pieces with the same base, exponents are added.
 * 4) When dividing exponential pieces with the same base, exponents are subtracted.
 * 5) The order of magnitude of a number can be viewed as the exponent on ten in it's scientific notation form.

Real-life applications

 * 1) An ability to quickly compare orders of magnitude is useful in sciences like astronomy to help put scale on sizes and distances.
 * 2) Several of the problems in this exercise are real-life applications.