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There are several ways to use estimation to help you find an answer without being exact. Estimation is not intended to get you to the exact answer. The purpose is for you to have an idea what the exact answer should be close to so that after you perform an operation, you can know if your answer is reasonable or not.

One way to estimate an answer is called front-end estimation. Using this method you simply use the first digit in the number to help you quickly guess what the answer will be close to.
For example, in addition you might see a problem like . Using front-end estimation you could find out that the answer is close to .

If you were to use this technique with the multiplication problem , you would estimate the answer would be close to .
Another method for estimating answers uses rounding. Instead of simply using the first digit in a number, you round the number. This tends to give a little more accurate estimate. Using the same examples from above, you can see the difference in our estimates if we use rounding as our estimation method.
For our addition problem, we can round each number to the nearest hundred and get . Notice this is larger than our earlier estimate and a closer to the exact answer of 8515.

In the multiplication problem, we will use the same approach of rounding to the nearest hundred and get which is somewhat closer to the exact answer of 643,314.
You can see that the rounding method tends to get you a little closer to the actual answer and is a much better tool when working with fractions.

But keep in mind that our main goal with estimation is to be able to tell if an answer is reasonable.

Let's Practice: Suppose I am given the following problem:
A chemistry lab assignment calls for 3 3/4 cups of distilled water to conduct a particular experiment. There are gallon bottles (128 ounces = 16 cups) of distilled water in the lab. How many experiments can be conducted with one gallon bottle of distilled water?

The exact answer can be found by dividing .

However, if I estimate that each experiment takes about 4 cups and there are only 16 cups total, I know that about 4 experiments can be conducted with one bottle of distilled water. In a practical setting of a chemistry lab, it would be much more valuable to estimate that four experiments could be done rather than having an exact answer.

Examples A student works at a job where she makes \$6.19 an hour and one week she works 37 hours. She receives her paycheck and it is for \$138 before taxes are taken out. She immediately suspects that her check is not for the correct amount. What should her check have been? What is your answer?  Suppose in a science class you are asked to make the following calculation: Use order of operations, the rules of exponents, and scientific notation to estimate a reasonable order of magnitude for your answer. What is your answer? S Taylor

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