Question

Using abbreviations and the rules of the metric system, express the following quantities correctly. Five thousandths of a gram ______

Short answer

5 mg

Step-by-step solution

Understanding the Quantity

The quantity given is 'five thousandths of a gram'. In decimal form, this is expressed as 0.005 grams.

Recognizing the Metric Prefix

In the metric system, the prefix 'milli-' denotes one thousandth, or 0.001 of a unit. Therefore, 'five thousandths of a gram' can be expressed using the 'milli-' prefix.

Applying the Metric Prefix

To convert 0.005 grams to the metric abbreviation, recognize that 0.005 is equivalent to 5 times 0.001 grams. Use the 'milli-' prefix for 0.001, so: \( 0.005 ext{ g} = 5 \times 0.001 ext{ g} = 5 ext{ mg} \).

Final Expression

The correct metric expression for five thousandths of a gram, using the abbreviation and the rules of the metric system, is 5 mg (milligrams).

Key concepts

Decimal Form

Decimal form is a way of expressing numbers using the base ten system, which is the foundation of our numeric understanding. When you see a number like 0.005, it means you have 5 parts out of 1000, or five thousandths.
Using decimal form allows us to easily see the relationship between parts and the whole. In our example, stating 0.005 grams helps to precisely define how much of a gram we have. The decimal point plays a crucial role as it separates the whole number part from the fractional part.

• The digit to the right of the decimal determines tenths, hundredths, thousandths, etc.
• For example, in 0.005: '0' is the whole number, '005' is the decimal part representing thousandths.
• Understanding decimal form is key to interpreting and displaying accurate measurements in many fields.

Metric Prefixes

The metric system uses prefixes to denote different magnitudes of units. These prefixes make it simpler to understand and communicate measurements without long numbers. Each prefix stands for a specific factor of ten.
In our exercise, the prefix 'milli-' indicates thousandths, or one-thousandth (0.001) of a base unit. This means if you have a measure in "milli-" units, you divide the base unit by 1,000.

• Kilo- (k) means 1,000 times the base unit.
• Mega- (M) means 1,000,000 times the base unit.
• Milli- (m) means 0.001 times the base unit, as used in our example of converting grams to milligrams.

These prefixes provide a straightforward way for interacting with and converting measurements, making scientific calculations clearer.

Abbreviations

Abbreviations in the metric system are a way to write measurements concisely while maintaining clarity. They are standardized letter shortcuts that represent complete units or terms.
For example, instead of writing 'milligram,' we use the abbreviation 'mg,' which is easier to remember and takes up less space. A few, useful metric system abbreviations include:

• 'g' for gram, the base unit of mass in the metric system.
• 'kg' for kilogram, which is 1,000 grams.
• 'L' for liter, a unit of volume.

Using these abbreviations helps in communicating scientific and everyday measurements efficiently.

Milligram Conversion

Converting units to milligrams involves applying the metric prefix 'milli-' to a base measurement, such as grams, to indicate thousandths. To convert from grams to milligrams, multiply the amount in grams by 1,000, because 1 gram equals 1,000 milligrams.
This conversion is essential in numerous scientific and pharmaceutical contexts where precision is crucial. In the given exercise:

• Start with 0.005 grams.
• 0.005 grams converted to milligrams is done by multiplying by 1,000. Therefore, 0.005 grams becomes 5 milligrams.
• The calculation can be summarized as: \( 0.005 \text{ g} = 0.005 \times 1000 \text{ mg} = 5 \text{ mg} \)

This conversion process allows for a more practical understanding and notation of tiny mass measurements.