Problem 22 - Calculate With Confidence

Question

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

Step-by-Step Solution

Answer

6 cg

Step 1: Understand the Metric Prefix

In the metric system, the prefix for 'hundredths' is 'centi-'. In this case, you want to use the abbreviation for 'centi-' which is 'c’.'

Step 2: Express in Grams with the Centi- Prefix

Since you are dealing with grams and need to express six hundredths of a gram, it translates to 'centigrams'. The abbreviation for centigram is 'cg' based on the centi- prefix and the base unit gram.

Step 3: Calculate the Quantity in Centigrams

Since six hundredths is equivalent to 6 centigrams, you can write this as 6 cg.

Key Concepts

Understanding Metric Prefixes

The metric system is a decimal-based system of measurement that uses various prefixes to denote different scales or quantities. Each prefix in the metric system indicates a specific factor of 10, making it easy to convert between larger and smaller units. One common metric prefix is "centi-," which means one-hundredth ( 10^{-2} ). This prefix is applied when we need to divide the base unit (such as a meter or gram) by 100. For example, 1 centimeter ( 1 ext{ cm} ) is one-hundredth of a meter. Similarly, 1 centigram ( 1 ext{ cg} ) is one-hundredth of a gram. This understanding allows you to convert measurements by simply moving the decimal point two places when converting from the base unit to the 'centi-' scaled version. This feature of the metric system makes calculations simple and consistent.

Using Abbreviations

Abbreviations play a crucial role in the metric system, making measurements more concise and easier to communicate. Each metric prefix has a specific abbreviation, often derived from the word for the prefix.

• "Centi-" is abbreviated as "c".
• "Gram" is abbreviated as "g".

When combining these, the abbreviation for "centigrams" becomes "cg", where "c" stands for the centi- prefix and "g" for grams. Using such abbreviations helps in avoiding lengthy writing and simplifies scientific notation.

The Concept of Centigrams

A centigram is a unit of mass measurement in the metric system. It is part of the smaller metric units of weight, which include

• milligrams (mg),
• centigrams (cg), and
• decigrams (dg).

One centigram ( 1 ext{ cg} ) is equivalent to one-hundredth ( 0.01 ) of a gram, and it is useful in measuring smaller quantities where grams might be too large of a unit. Expressing mass in centigrams is particularly common in scientific fields and areas requiring precision. Conversion Example: To convert grams to centigrams, simply multiply the number of grams by 100. For instance, 0.06 grams is equivalent to 6 centigrams, making this unit ideal for more detailed and precise measurements when dealing with smaller mass quantities.