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Chapter 1: Problem 12

Determine the precision of each measurement. \(10.30 \mathrm{~cm}\)

Short Answer

Expert verified
The precision is to the nearest hundredth of a centimeter.

Step by step solution

01

Understanding Precision

Precision in a measurement refers to the smallest unit to which a measurement is made. In measurement terms, it indicates how exact or detailed the measurement is.
02

Identify the Smallest Unit

Look at the given measurement, which is written as \(10.30 \mathrm{~cm}\). The smallest digit affected by uncertainty is the last digit, which is the hundredths place in this measurement.
03

Determine the Precision

Since the smallest unit in the measurement \(10.30 \mathrm{~cm}\) is the hundredths place, the precision is to the nearest hundredth of a centimeter.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Significant Figures
Significant figures in a measurement reflect the digits that carry meaningful information regarding its precision. In the measurement \(10.30 \mathrm{~cm}\), each digit communicates something about the accuracy of the measurement. This includes
  • Known digits: \(10\) and \(3\)
  • An estimated digit: \(0\) in the hundredths place
The rules of significant figures help students determine which numbers are important for representing the precision of the measurement. For \(10.30 \mathrm{~cm}\), it includes the digit '1' (tens), '0' (ones), '3' (tenths), and the final '0' (hundredths), which is significant because it indicates a level of detail to the nearest hundredth.
Measurement Accuracy
Measurement accuracy describes how close a measurement is to the actual or true value. Accurate measurements rely heavily on correctly identifying significant figures to provide an accurate reflection of the measurement鈥檚 true value.
In the example of \(10.30 \mathrm{~cm}\), this implies:
  • The instrument used was capable of measuring to the nearest hundredth of a centimeter.
  • There was consistency and care taken in the measurement process to ensure this accuracy.
This ensures that the values are not overestimated or underestimated, balancing precision with reality.
Educational Physics
Educational physics often emphasizes understanding measurements, units, and the precision of different quantities. Becoming adept at these foundational concepts allows students to solve physics problems accurately and efficiently.
With practical exercises, like measuring \(10.30 \mathrm{~cm}\), students practice determining the precision and accuracy of measurements.
  • Techniques such as estimating significant figures teach clear communication of results.
  • Understanding measurement accuracy helps students evaluate the reliability of their results.
These skills are essential in all scientific fields, where precise and accurate measurements form the basis of sound scientific inquiry and analysis.

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Most popular questions from this chapter

Determine the accuracy (the number of significant digits) of each measurement. \(2.4 \times 10^{3} \mathrm{~kg}\)

In each set of measurements, find the measurement that is (a) the least accurate and (b) the least precise. \(27.5 \mathrm{~m} ; 0.65 \mathrm{~m} ; 12.02 \mathrm{~m}\)

Change 1 h 25 min to min.

In each set of measurements, find the measurement that is (a) the least accurate and (b) the least precise. \(45,000 \mathrm{~N} ; 250 \mathrm{~N} ; 16.8 \mathrm{~N} ; 0.25 \mathrm{~N} ; 3 \mathrm{~N}\)

Determine the precision of each measurement. \(5 \overline{0} 0 \mathrm{~g}\)
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