Problem 77 - Prealgebra

Question

In Exercises 77-82, use a calculator to approximate the square root to the nearest tenth. \(\sqrt{469}\)

Step-by-Step Solution

Answer

\(\sqrt{469} \approx 21.7\)

Step 1: Identify the Problem

We need to approximate the value of \( \sqrt{469} \) using a calculator and round the result to the nearest tenth.

Step 2: Use a Calculator

Input \( \sqrt{469} \) into a calculator to find its approximate decimal value. The calculator displays approximately 21.63330765.

Step 3: Round to the Nearest Tenth

Look at the first decimal place, which is 6 in 21.63330765. Since it is greater than or equal to 5, we round up the tenths place from 2.6 to 2.7.

Key Concepts

Efficient Use of Calculator

Calculators are invaluable tools when you need to handle complex operations quickly.
If you're working with square roots, like in our example with \( \sqrt{469} \), they help by providing precise calculations. Knowing how to enter and interpret the results from your calculator efficiently is beneficial. Most scientific calculators have a square root function, usually represented by a \( \sqrt{ } \) symbol. Simply press this button, followed by the number you need the root of.

• Ensure your calculator is in the correct mode (degree/radian) if required.
• Double-check your input to avoid common mistakes like using a wrong number.
• Trust the displayed result, but be prepared to round it appropriately in the next steps.

Using a calculator correctly saves time and reduces errors in mathematical exercises.

Rounding Numbers Effectively

Rounding numbers is a technique often used in math to simplify numbers to make them easier to work with. It's crucial to understand which place value is affected by rounding.
When you have a number like 21.63330765 from your calculator, knowing how to round is key. The general rule is to look at the digit to the right of the place you're rounding to. For example, when rounding to the nearest tenth:

• Identify the tenths place (the first decimal place).
• Check the digit after it (6 in this case).
• If it's 5 or more, round up; if less, round down.

This means 21.63330765 becomes 21.7. Always remember, rounding makes numbers simpler while still keeping them close to the original value.

Understanding Decimal Places

Decimal places are the digits found to the right of a decimal point.
Understanding them is essential for precise calculations and rounding practices.
In our previous example, 21.63330765 is a decimal number representing the approximate square root of 469. Here, 21 is the whole number part, and 63330765 is the decimal part.

• The first number right after the decimal is the tenths place.
• The second is the hundredths place.
• The third is the thousandths place, and so on.

Knowing these positions helps in determining where and how precisely to round a number. This detailed grasp of decimal places ensures your approximations remain accurate, especially in scientific and mathematical contexts.