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Chapter 1: Problem 23

A measurement is a quantitative observation involving both a number and a unit. What is a qualitative observation? What are the SI units for mass, length, and volume? What is the assumed uncertainty in a number (unless stated otherwise)? The uncertainty of a measurement depends on the precision of the measuring device. Explain.

Short Answer

Expert verified
A qualitative observation is an observation that describes properties or characteristics of an object without involving numerical values. The SI units for mass, length, and volume are the kilogram (kg), meter (m), and cubic meter (m³), respectively. The assumed uncertainty in a measurement is one-half of the least significant digit, and it depends on the precision of the measuring device. A more precise measuring device results in a smaller uncertainty in the measurement.

Step by step solution

01

Definition of Qualitative Observation

A qualitative observation is an observation that is made without resulting in a numerical value. Instead, it focuses on descriptions, properties, or characteristics of an object or phenomenon. For example, describing the color or texture of an object would be a qualitative observation.
02

SI Units for Mass, Length, and Volume

The SI units (International System of Units) for mass, length, and volume are as follows: 1. Mass: The SI unit for mass is the kilogram (kg). 2. Length: The SI unit for length is the meter (m). 3. Volume: The SI unit for volume is the cubic meter (m³). Note that volume can also be expressed in terms of the unit liters (L), where 1 m³ = 1000 L.
03

Assumed Uncertainty in a Measurement

The assumed uncertainty in a measurement is a small range around the measured value that indicates the possible error or variation when taking a measurement. In general, if the uncertainty is not explicitly stated, we should assume a relative uncertainty of one-half of the least significant digit. For instance, if a measurement is given as 5.2 cm, we should assume a possible uncertainty of ±0.05 cm.
04

Uncertainty and Precision of the Measuring Device

The uncertainty of a measurement is directly related to the precision of the measuring device being used. A more precise measuring device will have a smaller uncertainty, meaning that the measurements it provides are closer to the true value of the quantity being measured. For example, if we were measuring the length of an object with a ruler marked in centimeters, we might have an uncertainty of ±0.5 cm. However, if we were using a caliper marked in millimeters, our uncertainty would be reduced to ±0.05 cm. This shows that the precision of the measuring device plays a crucial role in determining the uncertainty of the measurement.

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