The diameter of the Earth at the equator is 7926.381 mi. (a) Round off this quantity to four significant figures and then to two significant figures.

Verified step by step guidance

1. Identify the number of significant figures required for rounding: four significant figures and two significant figures.
2. For four significant figures, start from the leftmost non-zero digit and count four digits. Round the fourth digit based on the fifth digit.
3. For two significant figures, start from the leftmost non-zero digit and count two digits. Round the second digit based on the third digit.
4. Apply the rounding rules: if the digit to be removed is 5 or greater, increase the last retained digit by one; if it is less than 5, leave the last retained digit unchanged.
5. Express the rounded numbers, ensuring that the number of significant figures matches the requirement.

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 ensuring that calculations reflect the precision of the data.

Rounding Rules

Rounding rules dictate how to adjust numbers to a specified level of precision. When rounding, if the digit immediately after the last significant figure is 5 or greater, the last significant figure is increased by one. If it is less than 5, the last significant figure remains unchanged. Mastery of these rules is essential for correctly rounding numbers to the desired significant figures.

Measurement and Precision

Measurement refers to the process of quantifying physical quantities, while precision indicates the degree of reproducibility of measurements. In scientific contexts, it is important to express measurements with the appropriate number of significant figures to convey the level of uncertainty. This ensures that the reported values are meaningful and reflect the limitations of the measuring instruments used.