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Chapter 1: Problem 32

Express the following SI units in symbol form: nanometer

Short Answer

Expert verified
The symbol for nanometer is "nm".

Step by step solution

01

Identify the SI prefix for nano

The SI prefix for "nano" is \(10^{-9}\). In symbol form, this can be denoted by the letter 'n'.
02

Recall that the meter is the base unit for length

In the International System of Units (SI), the base unit for length is the meter. The symbol for the meter is 'm'.
03

Combine the symbols

Now that we have both the SI prefix (n) and the base unit of length (m), we can combine them to express the SI unit nanometer in symbol form. The combined symbols for nanometer are "nm".

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Key Concepts

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

Metric System
The metric system is an international decimal system of measurement that is commonly used around the world. Originating from France, it was designed to make calculations easy and consistent. The system uses base units like the meter for length, the kilogram for mass, and the second for time.
These base units can be extended by prefixed units to represent smaller or larger quantities, making it highly versatile. This is why the metric system is preferred in scientific fields and by most countries for daily use.

Benefits of the metric system include:
  • Ease of conversion: All units are based on powers of ten, making them easy to convert.
  • Universally recognized: Used internationally, facilitating global communication and trade.
  • Consistency across measurements: Provides a standardized way to measure, which is critical in scientific research.
Unit Conversion
Unit conversion is the process of converting a quantity expressed in one unit to another unit without changing its value. In the metric system, conversions are straightforward due to the use of prefixes that denote powers of ten.
To convert between metric units, you utilize the simple principle of multiplying or dividing by powers of ten. For example, converting millimeters to meters involves dividing by 1,000, since a millimeter (mm) is one thousandth of a meter (m).

Here are some simple steps for unit conversion in the metric system:
  • Identify the units you are converting between.
  • Determine the conversion factor, which relates the two units.
  • Multiply or divide the original measurement by the conversion factor to find the equivalent measurement in the new unit.
SI Prefixes
SI prefixes are an essential part of the metric system, allowing users to express very small or very large quantities succinctly. Each prefix denotes a specific power of ten, simplifying everything from scientific notation to everyday measurements.
"Nano" is one of these prefixes and represents the factor of \(10^{-9}\). This means one nanometer is one billionth of a meter. Common SI prefixes and their corresponding factors include "kilo" (\(10^3\)), "centi" (\(10^{-2}\)), and "milli" (\(10^{-3}\)).

SI prefixes:
  • Make calculations more manageable by reducing the number of zeroes you have to write out.
  • Provide a universal shorthand for large and small numbers, enhancing communication in science and engineering.
  • Facilitate easier understanding and memorization of measurements.

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