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When we say that we are approximating decimals, we are talking about getting close to the exact decimal value without necessarily hitting it perfectly. This is especially handy for non-terminating decimals. In our example, the square root of 8 cannot be represented as a simple fraction. The number we get from the calculator will have many digits, and approximating means finding a shorter version that is 'close enough' for practical purposes. This makes our calculations easier and quicker. For instance, instead of using the full display of \(\text{2.828427124}\), we can approximate it to \(\text{2.828}\). Approximating decimals helps in making the problem solution more manageable while still maintaining a high level of accuracy.

Calculators are powerful tools that help in making complex calculations easier and more accurate. To find the square root of a number like 8, you first need to turn on your calculator. Here's a quick guide:

• Enter the number you want to find the square root of, in this case, 8.
• Find and press the square root button (usually marked as \( \sqrt{}\)).

The display will now show the square root of 8. It's handy to note down all the digits shown by the calculator because the more digits you record, the more accurate your approximations and further calculations will be. Using a calculator simplifies and speeds up the process, especially when dealing with irrational numbers like \(\text{2.828427124}\).

Rounding numbers involves reducing the number of digits in a number while keeping its value close to what it was. Let's take the example of the square root of 8, which is \(\text{2.828427124}\). We want to approximate it to three decimal places. Here is how you do it:

• Identify the first three digits after the decimal point, which are '828' in \(\text{2.828427124}\).
• Look at the fourth digit after the decimal point, which is '4'.
• If this digit is 5 or above, we round up the last digit of '828'. However, since it is less than 5, we'll round down.

Thus, \(\text{2.828427124}\) rounded to three decimal places becomes \(\text{2.828}\). This method ensures that our approximations are both simple and effective, reducing calculation complexity without losing significant accuracy.