Why should we estimate before solving a problem?
We should estimate before solving a problem to make sure our answer is close to the real answer.
Here's a simple problem.
Suppose we want to find wnat a 6% tax on a $10 purchase would be. When you do the math, the answer depends upon where you place the decimal point when you multiply .06 x $10.
You need to estimate what is a reasonable tax on a $10 purchase -- 6 cents? 60 cents? 6 dollars?
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Estimating before solving a problem helps us in several ways:
1. It gives us a rough idea of what to expect as the answer. This can help us gauge the reasonableness of our final answer. In the example you provided, estimating whether the tax on a $10 purchase would be 6 cents, 60 cents, or 6 dollars helps us identify which range the answer should fall into.
2. It helps us catch potential mistakes. By estimating before solving the problem, we can quickly determine if our final answer is way off base. If our estimation suggests that the answer should be around 6 cents, but our calculation gives us 6 dollars, we know that we have made a significant error and need to reevaluate our approach.
3. It allows for a quicker solution. Estimating often involves simplifying the problem or rounding numbers, which can make calculations easier and quicker. This is especially useful when dealing with complex or time-sensitive problems.
In the given problem, to estimate what a 6% tax on a $10 purchase would be, you can simply calculate 6% of $10 in your head without worrying about the precise decimal placement.
Using mental math, you can estimate the tax on a $10 purchase to be around 60 cents.