Question

Give the prefix that represents each multiplier. a) \(1 / 1,000\) th \(\times\) b) \(1,000 \times\) c) \(1,000,000,000 \times\)

Short answer

(a) milli, (b) kilo, (c) giga

Step-by-step solution

Identify the Multiplier for Part (a)

For the multiplier \( \frac{1}{1,000} \), we need to recognize that this represents a factor of \( 10^{-3} \). In the International System of Units (SI), the prefix associated with \( 10^{-3} \) is 'milli'. Therefore, the prefix for \( \frac{1}{1,000} \) is 'milli'.

Identify the Multiplier for Part (b)

For the multiplier \( 1,000 \), we know that this represents a factor of \( 10^3 \). In the SI system, the prefix for \( 10^3 \) is 'kilo'. Thus, the prefix for \( 1,000 \) is 'kilo'.

Identify the Multiplier for Part (c)

For the multiplier \( 1,000,000,000 \), it represents a factor of \( 10^9 \). The SI prefix that corresponds to \( 10^9 \) is 'giga'. Therefore, the prefix for \( 1,000,000,000 \) is 'giga'.

Key concepts

Metric System

The metric system is a universal language used in science, industry, and everyday life internationally. It is designed on a decimal system where each unit is based on factors of ten. This makes it simple to convert between units because you're essentially just moving the decimal point.

In the metric system, length is measured in meters, mass in kilograms, and volume in liters. Each of these base units can be modified with prefixes to indicate different magnitudes. For example:

• "Kilo-" represents 1,000 times the base unit.
• "Milli-" represents 1/1,000 of the base unit.
• "Giga-" represents 1,000,000,000 times the base unit.

By understanding these basic principles of the metric system, converting and working with different units becomes straightforward and intuitive.

Multipliers

Multipliers are essential in adapting unit sizes to match the quantity being measured. They help in expressing large or small values more conveniently. In mathematics, multipliers transform a number by multiplying it by a given factor.

Consider the following multipliers as examples:

• For the multiplier \( \frac{1}{1,000} \), or \( 10^{-3} \), the SI prefix used is "milli," which signifies a thousandth of the unit.
• The multiplier \( 1,000 \) or \( 10^3 \) corresponds to "kilo," indicating a unit multiplied by a thousand.
• With a multiplier of \( 1,000,000,000 \) or \( 10^9 \), the prefix "giga" indicates a billion times the unit.

These multipliers help streamline communication in science and technology, making it easier to express large and small values effectively.

International System of Units

The International System of Units (SI) is the modern form of the metric system, widely used around the world. It serves as a standardized system of measurement and is essential for global communication in science, engineering, and trade.

An important aspect of SI is its set of prefixes, which represent powers of ten, simplifying the representation of very large or very small quantities:

• Prefixes like "kilo," "milli," and "giga" correspond to power factors like \( 10^3 \), \( 10^{-3} \), and \( 10^9 \), respectively.

The SI is built upon seven base units, including the meter, kilogram, and second, which form the foundation of the system. By using SI units, scientists and professionals can ensure clarity and precision in their work across different countries and disciplines.