Question

For Exercises \(1-16\), match the power of 10 to its name or use. A. \(10^{-12}\) B. \(10^{-9}\) C. \(10^{-6}\) D. \(10^{-3}\) E. \(10^{3}\) F. \(10^{6}\) G. \(10^{9}\) H. \(10^{12}\) I. \(10^{15}\) $$ \text { Micro- } $$

Short answer

"Micro-" corresponds to \(10^{-6}\).

Step-by-step solution

Identify the prefix for "Micro-"

The prefix "Micro-" is used in the metric system to denote a factor of one millionth, or \(10^{-6}\). This is a common prefix that is often used in scientific measurements, such as in micrograms (\(\mu g\)) or micrometers (\(\mu m\)).

Match the prefix to the power of 10

Looking at the list of options provided, option C corresponds to \(10^{-6}\). Therefore, the power of 10 that matches the prefix "Micro-" is \(10^{-6}\).

Key concepts

Scientific Measurements

Scientific measurements are essential in providing accurate and precise data across various scientific fields. Measurement is a fundamental aspect of science because it allows scientists to collect quantitative data. This data can then be analyzed, compared, and used to draw conclusions. There are several properties that scientific measurements require:

• Accuracy: This refers to how close a measurement is to the true value. Without accuracy, results may lead to incorrect conclusions.
• Precision: This indicates the repeatability or consistency of measurements. High precision means that if the measurement is repeated, the results will be very similar.
• Units: Units are standardized quantities used to express and communicate measurements.

Scientific instruments often use sensors and tools calibrated to the metric system. This system simplifies scientific measurements, as it is universally recognized and based on powers of ten, allowing easy conversion between larger and smaller units.

Metric Prefixes

The metric system uses prefixes to express measurements in a more manageable format. These metric prefixes are standardized across the world, making them crucial for scientific and international communication.
The prefix you use depends on the size of the measurement. There are prefixes for both very large and very small numbers.

• Kilo-: Represents a factor of 1,000 ( 10^{3} ).
• Mega-: Joins values by a factor of 1,000,000 ( 10^{6} ).
• Giga-: Indicates a factor of 1,000,000,000 ( 10^{9} ).
• Micro-: Indicates a factor of 0.000001 ( 10^{-6} ).
• Nano-: Denotes a factor of 0.000000001 ( 10^{-9} ).
• Pico-: Defines a factor of 0.000000000001 ( 10^{-12} ).

Using these prefixes simplifies the recording and understanding of scientific data. They help avoid using excessively large numbers or microscopic decimals and make calculations more straightforward.

Powers of Ten

Understanding the powers of ten is integral to working with scientific measurements and the metric system. Powers of ten simplify the expression of both very large and very small numbers, easing calculation and comprehension. The format 10^{n} is used to express a number as a power of ten, where 'n' is an integer.

• If 'n' is positive, the power of ten represents a large number. For example, 10^{3} is 1,000.
• If 'n' is negative, it signifies a fraction, such as 10^{-6} representing one millionth (0.000001).

This system of powers of ten allows for the expression of any number using a base of ten, which is the foundation for the metric system and scientific notation.
By consistently using these expressions, scientists and engineers streamline calculations, making them easier to comprehend and communicate.