How many significant figures are in each of the following measurements? (e) 67,000 m²

Verified step by step guidance

1. Identify the given measurement: 67,000 m^2.
2. Determine if there is a decimal point present in the number. In this case, there is no decimal point.
3. Recognize that without a decimal point, trailing zeros are not considered significant.
4. Count the non-zero digits, which are significant. Here, '67' are the non-zero digits.
5. Conclude that the number of significant figures in 67,000 m^2 is 2.

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 only when there is a decimal point. Understanding significant figures is crucial for accurately reporting measurements in scientific contexts.

Rules for Counting Significant Figures

There are specific rules for determining the number of significant figures in a measurement. For example, leading zeros are not counted, while captive zeros (zeros between non-zero digits) are significant. Trailing zeros are significant only if the number contains a decimal point, which is essential for interpreting the precision of the measurement.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a more manageable form, typically in the format of 'a × 10^n', where 'a' is a number between 1 and 10, and 'n' is an integer. This notation helps clarify the number of significant figures, especially in cases where trailing zeros may be ambiguous in standard decimal notation.