Question

Using abbreviations and the rules of the metric system, express the following quantities correctly. Four and two tenths micrograms ______

Short answer

4.2 µg

Step-by-step solution

Understand Micrograms in the Metric System

In the metric system, the prefix 'micro-' stands for one-millionth of a unit, or \( 10^{-6} \). This means that a microgram (µg) is \( 10^{-6} \) grams.

Convert Decimals to Numbers

The phrase "four and two tenths" represents the decimal number 4.2.

Combine Number and Unit with Abbreviation

Combine the numerical value 4.2 with the abbreviation for micrograms, which is 'µg'. The correctly expressed quantity is written as 4.2 µg.

Key concepts

Micrograms

Micrograms are a small unit of measurement in the metric system, primarily used to measure very light weights. This unit is especially useful in scientific fields like chemistry and biology, where precision is critical. The prefix "micro-" indicates that a microgram is one-millionth of a gram. This prefix can be used across many metric units, but here, it specifically refers to weight. To put it in perspective, there are one million micrograms in one gram, making it much smaller than the more commonly used milligram.

• 1 Microgram (µg) = 0.000001 Grams (g)
• The symbol for microgram is µg, combining the Greek letter 'mu' (µ) and 'g' for gram.

Using micrograms helps us express tiny amounts conveniently, without resorting to lengthy decimal numbers.

Decimal Conversion

Decimal conversion involves changing spoken or written numerical expressions into their decimal form. This skill is particularly useful in math and science for standardizing numbers for calculations and data representation. It provides a straightforward way to express values that aren't whole numbers. Take for instance the phrase "four and two tenths." This converts directly to the decimal number 4.2. In a decimal number:

• The number to the left of the decimal point represents whole units.
• The numbers to the right represent parts of a whole, based on place value such as tenths, hundredths, etc.

When converting verbal expressions to decimals, it’s crucial to identify the respective place values accurately, ensuring correct representation of the quantity.

Abbreviations

Abbreviations are shortened forms of words or phrases, often used to save space and time in communication. In the scientific context, abbreviations serve to standardize units of measurement, making them easier to use and understand across different regions and languages. The abbreviation for microgram is µg. Here, 'µ' represents the micro- prefix, and 'g' stands for grams. Using the abbreviation avoids repeated lengthy terms, especially in scientific calculations and documentation. Recognizing and understanding abbreviations is essential in scientific studies to ensure accurate interpretation of measurements.

Scientific Notation

Scientific notation is a method of writing numbers that are too large or too small to be conveniently written in decimal form. It is especially useful in science and engineering fields. It enables easy reading and interpretation of values by expressing them as a product of a number between 1 and 10 and a power of 10.For example:

• The number 0.000001 grams can be expressed in scientific notation as \(1 \times 10^{-6}\) grams.
• This readability makes it easier to perform calculations with very large or small numbers without errors.

Understanding scientific notation is crucial for working efficiently with the metric system, since it simplifies complex numerical expressions. It also helps in identifying and converting prefixes like micro- more effectively by relating them to powers of ten.