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Chapter 2: Problem 5

Indicate what multiplier each prefix represents. a) \(\mathrm{k}\) b) \(m\) c) \(\mathrm{M}\)

Short Answer

Expert verified
\(\mathrm{k} = 10^3\), \(m = 10^{-3}\), \(\mathrm{M} = 10^6\).

Step by step solution

01

Understanding the Metric Prefixes

Metric prefixes are used in the International System of Units to represent powers of ten. Each prefix stands for a specific multiplier. Our task is to identify these multipliers for the given prefixes: \( \mathrm{k} \), \( m \), and \( \mathrm{M} \).
02

Determining the Multiplier for 'k'

The prefix \( \mathrm{k} \) stands for 'kilo.' It indicates a multiplier of 1,000 or \( 10^3 \). So anything that uses the 'kilo' prefix will be 1,000 times the base unit.
03

Determining the Multiplier for 'm'

The prefix \( m \) stands for 'milli.' It represents a multiplier of 0.001 or \( 10^{-3} \). This means that 'milli' makes the unit a thousandth of the base unit.
04

Determining the Multiplier for 'M'

The prefix \( \mathrm{M} \) stands for 'mega.' It corresponds to a multiplier of 1,000,000 or \( 10^6 \). Therefore, using 'mega' makes the unit a million times the base unit.

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Key Concepts

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

Kilo Prefix Multiplier
The prefix "kilo," abbreviated as \( \mathrm{k} \), plays a significant role in the metric system. It indicates a multiplier of 1,000, or mathematically, \( 10^3 \). This means whenever you see the prefix "kilo," the value is 1,000 times the base unit. Think of the word "kilometer" where each kilometer is 1,000 meters. It's like if we had a magnifying glass that could zoom in a thousand times, providing us with larger, more comprehensible units.
  • Kilo- always multiplies the base unit by 1,000.
  • Used for substantial measurements, such as kilometers, kilograms, and kilowatts.
This makes the "kilo" very handy for expressing larger quantities within everyday use, providing clarity in measurements.
Milli Prefix Multiplier
Understanding the prefix "milli," represented by the letter \( m \), is vital in mastering metric conversions. "Milli" signifies a tiny scale multiplier of 0.001, or \( 10^{-3} \). It's as if we have an ant-sized measurement, providing a small fraction of the base unit. For instance, in millimeters, each millimeter is one-thousandth of a meter.
  • Milli- divides the base unit by 1,000, effectively.
  • Often used when dealing with smaller or precise measurements, such as millimeters, milliliters, and milligrams.
This prefix allows us to handle minuscule amounts with ease, making it perfect for requirements demanding precision and accuracy.
Mega Prefix Multiplier
The term "mega," shown by \( \mathrm{M} \), is the big player in the world of metric prefixes. Standing for a multiplier of 1,000,000, or \( 10^6 \), "mega" takes any unit to a colossal scale. Imagine using a "mega lens" that expands units to one million times their original size. For example, a megabyte equals one million bytes, helping us manage vast data quantities.
  • Mega- scales the base unit up by 1,000,000 times.
  • Commonly applied to large-scale measurements, such as megawatts or megahertz.
"Mega" proves invaluable for representing larger-than-life figures, enhancing our ability to handle immensely large scale concepts with ease.

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Most popular questions from this chapter

Which has the greater volume, \(100.0 \mathrm{~g}\) of hydrogen gas \(\left(d=0.0000899 \mathrm{~g} / \mathrm{cm}^{3}\right)\) or \(25.0 \mathrm{~g}\) of argon gas \(\left(d=0.00178 \mathrm{~g} / \mathrm{cm}^{3}\right) ?\)

Perform the following conversions. a) \(45.0 \mathrm{~m} / \mathrm{min}\) to meters/second b) \(0.000444 \mathrm{~m} / \mathrm{s}\) to micrometers/second c) \(60.0 \mathrm{~km} / \mathrm{h}\) to kilometers/second

Why would it be inappropriate to convert from cubic meters to cubic seconds?

The coldest temperature ever recorded on the surface of the earth was \(-128.6^{\circ} \mathrm{F}\) in Vostok, Antarctica, in \(1983 .\) What is the temperature in degrees Celsius and in kelvins?

Perform the following conversions. a) \(4.701 \times 10^{15} \mathrm{~mL}\) to kiloliters b) \(8.022 \times 10^{-11} \mathrm{ks}\) to microseconds
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