Question

\(10^{2}\) multiple of a quantity is represented as (a) centi (b) \(\operatorname{deci}\) (c) hecto (d) deca

Short answer

The prefix representing \(10^{2}\) multiple of a unit is (c) Hecto.

Step-by-step solution

Identify the Prefixes

The first step is to recognize the prefix associated with each option. The prefixes for the options given are: (a) Centi, which represents \(10^{-2}\) or 0.01 of the base unit, (b) Deci, signifying \(10^{-1}\) or 0.1 of the base unit, (c) Hecto, representing \(10^{2}\) or 100 times the base unit and (d) Deca, denoting \(10^{1}\) or 10 times the base unit.

Compare with Given Quantity

The second step involves comparing the given quantity (\(10^{2}\)) with the multiples represented by each prefix. It's seen that Hecto corresponds to \(10^{2}\) or 100 times the base unit.

Choose the Correct Answer

Since the quantity given in the problem is \(10^{2}\), the corresponding metric prefix is Hecto. Therefore, the answer is (c) Hecto.

Key concepts

Understanding the Metric System

The metric system is a standardized method of measurement based on the power of ten. It is used globally for scientific and everyday measurements. This decimal-based system is designed to be simple and universal.

For any base unit in the metric system, such as a meter (length), gram (mass), or liter (volume), we use metric prefixes to represent quantities that are multiples or submultiples of these units. For example, the prefix 'kilo-' signifies one thousand units (like kilometers or kilograms), while 'milli-' represents one thousandth of a unit (like milliliters or milligrams).

In the given exercise, understanding metric prefixes is essential to identify the right multiple. 'Hecto-' is the correct prefix for a hundred-fold increase—the power of two when using ten as the base, which is precisely what is required to match the given quantity of \(10^{2}\).

Grasping SI Units

SI units, or the International System of Units, are the modern form of the metric system and the most widely used system of measurement. It comprises seven base units, which include the meter for length, kilogram for mass, second for time, and others.

These base units can be combined with metric prefixes to cover a vast range of measurements without the confusion of having entirely separate units for different scales. For example, distances in astronomy are measured in kilometers, gigameters, or even terameters, while distances in molecular biology are often in nanometers or micrometers—all utilizing the same base unit of the meter with different prefixes.

The use of SI units promotes clarity and consistency in science and technical communication. The exercise provided hones in on this concept by requiring students to match a quantity with the correct SI prefix to gain a better understanding of the relationship between the units and their practical application.

Deciphering Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is also used to simplify numbers when exactness is not crucial. A number in scientific notation is written as the product of a number between 1 and 10 and a power of 10.

For instance, the number 650 can be expressed as \(6.5 \times 10^{2}\) in scientific notation. This makes it easier to perform calculations, especially with very small or large numbers. Scientific notation also helps in understanding the significance of metric prefixes as they are associated with powers of ten.

By practicing with scientific notation and recognizing that 'hecto' corresponds to \(10^{2}\), students can see there is a direct correlation between the power of ten in the scientific notation and the magnitude of the metric prefix, streamlining the process of converting between different measurement scales.