Question

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

Short answer

0.4 mg

Step-by-step solution

Understand the Metric Prefix

In the metric system, the prefix 'milli-' means one-thousandth, which is denoted as \(10^{-3}\). Therefore, a milligram (mg) is \(10^{-3}\) grams. Understanding this allows you to correctly convert and express quantities in the metric system.

Express the Given Quantity in Numeric Form

The given quantity is four tenths of a milligram. First, express four tenths as a decimal: \(0.4\). Therefore, four tenths of a milligram is equivalently expressed as \(0.4\) mg.

Write the Quantity Using Metric Notation

The unit for milligrams in metric notation is 'mg'. Thus, four tenths of a milligram is written as \(0.4\) mg.

Key concepts

Metric Prefixes

In the metric system, understanding prefixes is essential for properly interpreting and expressing measurements. A metric prefix is a unit prefix that comes before a basic unit of measure to indicate a multiple or fraction of that unit. For example, 'milli-' is a common metric prefix, which signifies a factor of one-thousandth (1/1000) or \(10^{-3}\).

These prefixes simplify the way we express very large or very small quantities. Instead of writing 0.001 grams, we use the prefix 'milli-' and express it as 1 milligram (mg). This avoids confusion and makes our communications more efficient and precise.

• 'kilo-' means one thousand (\(10^3\)).
• 'centi-' denotes one hundredth (1/100 or \(10^{-2}\)).
• 'micro-' represents one millionth (1/1,000,000 or \(10^{-6}\)).

Familiarity with these prefixes allows you to convert between different metric units competently, ensuring accuracy in scientific and everyday measurements.

Unit Conversion

Unit conversion is the process of converting a measure from one unit to another. In the metric system, this often involves shifting the decimal point according to the metric prefixes. Specifically, metric conversions are straightforward because they are based on powers of ten.

For example, to convert from milligrams to grams, recognize that 1 milligram is \(10^{-3}\) grams. Therefore, to convert 0.4 milligrams to grams, we multiply by \(10^{-3}\):\[0.4 \times 10^{-3} = 0.0004 \text{ grams}\]

Here’s a simple guide to performing metric conversions:

• Identify the current unit and the unit you want to convert to.
• Determine the power of ten that relates the two units.
• Adjust the decimal point based on the power of ten.

Following this method ensures that you accurately translate quantities into the desired units.

Decimal Notation

Decimal notation is a way of representing numbers that uses powers of ten. This form of expression is fundamental to the metric system, as the entire system is based on multiples of ten.

When converting fractions, such as four tenths, to decimal form, you simply place the numerator over the denominator and divide:\[\frac{4}{10} = 0.4\]

The decimal 0.4 tells us that there are 4 parts out of a whole that is divided into 10 parts. Decimal notation is practical because it fits seamlessly with the metric system’s reliance on base ten. It simplifies calculations and conversions within the metric system.

Understanding how to read and write decimals is essential when working with measurements, as it helps ensure precise communication of quantities.

Measurement Units

Measurement units in the metric system provide standardized quantities for expressing physical quantities, such as length, mass, and volume. Each type of measurement has a base unit, which is then modified with prefixes to represent larger or smaller quantities.

For example:

• The base unit of mass is the gram (g).
• For length, it’s the meter (m).
• For volume, the base unit is the liter (L).

This system of units, known as the International System of Units (SI), ensures consistency and ease of understanding worldwide.

By using these standardized units, scientists and professionals around the globe can share and interpret data without confusion. This universal understanding is particularly crucial in fields like science, engineering, and medicine, where precise measurements are indispensable.