Is the use of significant figures in each of the following statements appropriate? (a) The 2005 circulation of National Geographic was 7,812,564.

Verified step by step guidance

1. Identify the context of the number: The circulation number is a count of items, which are whole numbers and not subject to significant figures in the same way as measured quantities.
2. Consider the precision of the number: Since this is a count, it is typically considered to have an infinite number of significant figures, as it is an exact number.
3. Evaluate the appropriateness of the number of digits: In this context, the number 7,812,564 is appropriate as it represents an exact count and not a measurement.
4. Discuss the difference between exact numbers and measured quantities: Exact numbers, like counts, are not limited by significant figures, unlike measurements which are subject to precision limitations.
5. Conclude on the appropriateness: The use of significant figures is not applicable here as the number is an exact count, not a measurement.

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 scientific contexts.

Precision vs. Accuracy

Precision refers to the consistency of repeated measurements, while accuracy indicates how close a measurement is to the true value. In the context of significant figures, a precise measurement will have a consistent number of significant figures, reflecting the reliability of the data collected.

Rounding Rules

Rounding rules dictate how to appropriately adjust numbers to reflect the correct number of significant figures. When rounding, if the digit to be dropped is less than five, the last retained digit remains unchanged; if it is five or greater, the last retained digit is increased by one. This ensures that the reported value maintains the intended precision.