Question

Write the numbers for these prefixes: (a) mega-,(b) kilo-, (c) deci-, (d) centi-, (e) milli-, (f) micro-, (g) nano-, (h) pico-.

Short answer

The values for the prefixes are (a) mega- \(\rightarrow 1 \times 10^6\), (b) kilo- \(\rightarrow 1 \times 10^3\), (c) deci- \(\rightarrow 1 \times 10^{-1}\), (d) centi- \(\rightarrow 1 \times 10^{-2}\), (e) milli- \(\rightarrow 1 \times 10^{-3}\), (f) micro- \(\rightarrow 1 \times 10^{-6}\), (g) nano- \(\rightarrow 1 \times 10^{-9}\), (h) pico- \(\rightarrow 1 \times 10^{-12}\)

Step-by-step solution

Identify and note the value for mega-

The prefix 'mega-' denotes a factor of one million, or \(1 \times 10^6\).

Identify and note the value for kilo-

The prefix 'kilo-' denotes a factor of one thousand, or \(1 \times 10^3\).

Identify and note the value for deci-

The prefix 'deci-' denotes a factor of one-tenth, or \(1 \times 10^{-1}\).

Identify and note the value for centi-

The prefix 'centi-' denotes a factor of one-hundredth, or \(1 \times 10^{-2}\).

Identify and note the value for milli-

The prefix 'milli-' denotes a factor of one-thousandth, or \(1 \times 10^{-3}\).

Identify and note the value for micro-

The prefix 'micro-' denotes a factor of one millionth, or \(1 \times 10^{-6}\).

Identify and note the value for nano-

The prefix 'nano-' denotes a factor of one billionth, or \(1 \times 10^{-9}\).

Identify and note the value for pico-

The prefix 'pico-' denotes a factor of one trillionth, or \(1 \times 10^{-12}\).

Key concepts

Scientific Notation

Scientific notation is a system used to express very large or very small numbers in a compact form. This notation makes calculations and comparisons easier. A number in scientific notation is written as the product of a number between 1 and 10 and a power of ten. For example, the number 6,000,000 can be written as \(6 \times 10^6\). The form is especially useful when dealing with quantities that vary across broad ranges, such as distances in astronomy or atomic scales in chemistry.

Some key points about scientific notation include:

• It simplifies the reading and writing of large numbers.
• The exponent tells you how many places the decimal point has been moved.
• It helps standardize the representation of numbers in scientific and engineering contexts.

When using scientific notation, remember that positive exponents denote large numbers, while negative exponents represent small numbers close to zero. Becoming familiar with this notation helps in understanding metric system prefixes, where each prefix corresponds to a power of ten.

Metric System

The metric system is a decimal-based system of measurement. It is used globally for almost all scientific and everyday measurements. The basis of the metric system is to provide a consistent way of quantifying different properties like length, mass, and volume. It is used extensively in science and industry around the world.

Metric units include meters for length, kilograms for mass, and liters for volume. What makes the metric system convenient is its use of prefixes. These prefixes denote multiples or fractions of a base unit, making the system adaptable for measuring both very large and very small quantities.

• Prefixes are consistent across all metric units. For instance, "kilo-" always means a thousand, no matter the unit.
• The use of ten as the base simplifies conversions, as you only need to move the decimal point.
• The system is coherent, meaning one unit of measure logically follows another.

Countries using the metric system often find it easier to engage in international trade and scientific research, as it underscores a common standard.

Metric Conversions

Metric conversions involve changing the measurement of a quantity from one metric unit to another. Thanks to the decimal foundation of the metric system, converting within this system often involves simple decimal point movements according to the prefixes involved.

Consider the following when working with metric conversions:

• Understanding powers of ten is crucial. Moving up a prefix like from "milli-" to "kilo-" involves moving the decimal point to the left (a decrease), while moving down involves moving it to the right (an increase).
• Common prefixes include "milli-" (\(10^{-3}\)), "centi-" (\(10^{-2}\)), "kilo-" (\(10^{3}\)), and "mega-" (\(10^6\)).
• Conversions are consistent across different measures, meaning a shift from a smaller to a larger prefix—or vice versa—is always by powers of ten.

For a practical example, converting 1500 millimeters to meters: remembering that "milli-" means one-thousandth, you would move the decimal three places to the left to find the equivalent in meters, making it 1.5 meters. Mastering metric conversions means being able to fluently navigate within a system that is not only simple but universally applicable.