Compute the following numbers, applying the significant figure rules adopted in this textbook.
$\sqrt{33.3}$

Verified step by step guidance

1. Identify the number of significant figures in the given value, 33.3. Since all digits are non-zero and the decimal point is present, it has 3 significant figures.
2. Recall the rule for significant figures when performing mathematical operations: For square roots, the result should have the same number of significant figures as the input value.
3. Set up the square root operation: \( \sqrt{33.3} \).
4. Perform the square root calculation while keeping track of significant figures. The raw result from the square root operation will need to be rounded to 3 significant figures.
5. Round the result of the square root to 3 significant figures, ensuring the final answer adheres to the significant figure rules.

Key Concepts

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for accurately reporting measurements and calculations in physics, as it reflects the precision of the data used.

Square Root Function

The square root function is a mathematical operation that finds a number which, when multiplied by itself, gives the original number. For example, the square root of 33.3 is a value that, when squared, equals 33.3. This operation is essential in various physics calculations, particularly in areas involving energy, motion, and wave phenomena.

Rounding Rules

Rounding rules dictate how to adjust numbers to reflect the correct number of significant figures. When a calculation results in a number with more significant figures than allowed, it must be rounded appropriately. For instance, if the result of sqrt(33.3) is 5.774, and only three significant figures are needed, it would be rounded to 5.77, ensuring the answer is both accurate and precise.