# Estimating Answers To Problems

## Estimate Answers by Rounding

Estimating answers to problems can be necessary if the calculations are to complex to perform
or if you need a quick answer (that does not have to be exact). By rounding numbers, you can
easily find answers to complex multiplication and division problems that you would otherwise
be unable to solve. The way to estimate using this method is very easy. Have a look at the example on the
right. The original mathematical expression is 213 x 301. This is impossible to do do without using long
multiplication which can take a long time. This is why we round to the closest unit, tenth, hundredth, etc.
depending on the degree of accuracy you require. In this case, we have rounded to the closest hundredth. This then gives us 200 x 300 which we can
easily calculate in our heads. Make sure that when writing your result us the almost equal sign (≈) instead of the normal equal
sign to show that the answer is an estimation. Underneath, you will find a couple of examples explaining this.
Finding Percentage Error
Now that you know how to estimate answers to division and multiplication problems, you can calculate the percentage error. This
allows you to analyse how far your estimation was off the actual result. Please share this page if you like it or found it helpful!
Example 1
In this example, we have rounded to the closest
tenth and were able to easily find the product of
90 and 110 which is an approximate answer to
the original problem.

Example 2
In this example, we have rounded to the closest
hundredth and were so able to find the
approximate solution to the problem.

Example 3
In this example, we have estimated a result to a division problem by rounding the numbers before dividing.
The original problem can only be solved using a calculator or long division.

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Chapter 5.1: Learning Outcomes
Students will be able to estimate answers to problems through rounding!
Students will be able to identify and apply the almost equal sign (≈)!

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