Question

Give the metric prefix that corresponds to each of the following: a. 1,000,000 b. \(10^{-3}\) c. \(10^{-9}\) d. \(10^{6}\) e. \(10^{-2}\) f. 0.000001

Short answer

a. Mega (M) b. milli (m) c. nano (n) d. Mega (M) e. centi (c) f. micro (µ)

Step-by-step solution

a. 1,000,000

The number 1,000,000 can be written as \(10^6\). The metric prefix for \(10^6\) is Mega (symbol: M). So, the metric prefix for 1,000,000 is Mega.

b. \(10^{-3}\)

The metric prefix for \(10^{-3}\) is milli (symbol: m). So, the metric prefix for \(10^{-3}\) is milli.

c. \(10^{-9}\)

The metric prefix for \(10^{-9}\) is nano (symbol: n). So, the metric prefix for \(10^{-9}\) is nano.

d. \(10^{6}\)

This is the same as the number given in part a. The metric prefix for \(10^6\) is Mega (symbol: M). So, the metric prefix for \(10^6\) is Mega.

e. \(10^{-2}\)

The metric prefix for \(10^{-2}\) is centi (symbol: c). So, the metric prefix for \(10^{-2}\) is centi.

f. 0.000001

The number 0.000001 can be written as \(10^{-6}\). The metric prefix for \(10^{-6}\) is micro (symbol: µ). So, the metric prefix for 0.000001 is micro.

Key concepts

Metric Prefixes

In the metric system, prefixes are utilized to denote various scales of measurement. These prefixes make it easier to express large or small numbers by reducing the number of zeros you have to write. Let's explore some key prefixes:

• Mega (M): Represents a factor of a million or \(10^6\). Any quantity like 1,000,000 can be expressed using this prefix, making it much more manageable.
• Milli (m): Corresponds to one-thousandth or \(10^{-3}\). It's very useful for expressing small measurements like a millimeter, which is a thousandth part of a meter.
• Nano (n): Represents \(10^{-9}\), meaning a billionth. Used commonly in areas like electronics to measure extremely small components.
• Centi (c): Denotes one-hundredth or \(10^{-2}\), commonly used in everyday terms like centimeters.
• Micro (µ): Equivalent to one-millionth or \(10^{-6}\), found in science and technology to measure minuscule distances.

These prefixes are standardized, making it easier for people all over the world to understand measurements without confusion.

Scientific Notation

Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in decimal form. It helps in expressing such numbers more concisely and is commonly used in scientific calculations.The format is simple:

• A number is expressed as the product of a number between 1 and 10, called the coefficient, and a power of ten. For example, the number 1,000,000 can be written as \(1 \times 10^6\).
• For small numbers like 0.000001, scientific notation would be \(1 \times 10^{-6}\). The negative exponent indicates the number's smallness.

Using this notation is crucial for precision and simplicity in fields like physics, chemistry, and engineering. It eliminates the lengthy writing of zeros and streamlines calculations. If you ever encounter very large or small numbers, writing them in scientific notation will make your life much easier.

Unit Conversion

Unit conversion is the process of converting a measure of physical quantity from one unit to another. This is a vital skill in science and engineering as it helps ensure consistency and accuracy when dealing with different measurement systems.Here’s a step-by-step way to perform unit conversion:

• Identify the conversion factor: Know the relationship between the units. For instance, 1 kilometer equals 1,000 meters.
• Multiply or divide: Use the conversion factor to switch between units. Multiply by the conversion factor to convert to a smaller unit or divide to convert to a larger unit.
• Check your work: Ensure that your final answer makes physical sense and that the units cancel accordingly.

For example, to convert 5 kilometers to meters, multiply by the conversion factor \(5 \times 1,000 = 5,000\) meters. Unit conversion is essential in everyday situations like cooking and traveling, as well as in scientific research and product development.