Measure the length of each of the objects in diagrams (a), (b), and (c) using the metric ruler in the figure. Indicate the number of significant figures for each and the estimated digit for each.
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Verified step by step guidance

1. Step 1: Observe the diagram and identify the object being measured. The object appears to be aligned with the metric ruler, starting at 0 cm and extending to a point between 7 cm and 8 cm.
2. Step 2: Determine the exact position of the object's endpoint. The endpoint is slightly past the 7 cm mark but does not reach the 8 cm mark. This requires estimating the position to the nearest tenth of a centimeter.
3. Step 3: Record the measurement with the correct number of significant figures. The ruler provides measurements to the nearest centimeter, and the estimated digit adds precision to the nearest tenth of a centimeter. For example, if the endpoint is estimated at 7.6 cm, the measurement would have three significant figures.
4. Step 4: Identify the estimated digit in the measurement. The estimated digit is the last digit in the recorded value, which is determined by visually estimating the position of the endpoint between the ruler's markings.
5. Step 5: Write down the final measurement, including the significant figures and the estimated digit. For example, if the measurement is 7.6 cm, the significant figures are '7' and '6', and the estimated digit is '6'.

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. When measuring, the number of significant figures indicates the certainty of the measurement, which is crucial for scientific accuracy.

Estimating Digits

Estimating digits refers to the practice of making an educated guess about the last digit of a measurement based on the precision of the measuring tool. For example, if a ruler measures to the nearest millimeter, the last digit may be estimated to the nearest half millimeter, reflecting the uncertainty in the measurement.

Metric Ruler Usage

A metric ruler is a tool used to measure length in centimeters and millimeters. It typically has markings that indicate these units, allowing for precise measurements. Understanding how to read a metric ruler is essential for accurately determining the length of objects and reporting measurements with the correct number of significant figures.