Question

Which would you rather have: a decigram of gold or a kilogram of gold?

Short answer

A kilogram of gold, because 1000 grams > 0.1 grams.

Step-by-step solution

Understand the Units

In this step, we will understand what each term means in terms of weight. A decigram (dg) is 1/10th of a gram, or 0.1 grams. A kilogram (kg) is 1000 grams. These are both units of weight where 1 kg > 1 dg.

Convert Decigrams to Grams

Next, let's convert the measure of gold from decigrams to grams. If a decigram is 0.1 grams, then a decigram of gold is exactly 0.1 grams.

Convert Kilograms to Grams

Now, let's convert the measure of gold from kilograms to grams. Since 1 kilogram equals 1000 grams, a kilogram of gold is 1000 grams.

Compare the Two Weights

Finally, we compare the two amounts: 0.1 grams (decigram of gold) versus 1000 grams (kilogram of gold). Since 1000 grams is much greater than 0.1 grams, a kilogram of gold is significantly heavier and more valuable than a decigram of gold.

Key concepts

Weight Comparison

When faced with determining which amount of gold is more valuable based on weight, it's essential to make a weight comparison. Compare the units directly to understand their respective scales.
In this exercise, we are comparing a decigram of gold to a kilogram of gold. Clearly, understanding the difference in magnitude is crucial.
We have:

• A extbf{decigram} (dg) is 0.1 grams, or one-tenth of a gram.
• A extbf{kilogram} (kg) is 1000 grams.

To perform a weight comparison, you must equate the units to the same scale — here, grams, so that you are comparing apples to apples. As evident in this comparison, 1000 grams (a kilogram of gold) is vastly larger than 0.1 grams (a decigram of gold).

Thus, the choice is clear; a kilogram of gold is far more substantial and valuable than a decigram.

Metric System

The metric system is a decimal-based system of measurement used internationally. It is crucial to understand this system when converting and comparing different units of weight and mass, as it simplifies calculations through its standardized conversion factors.
The basic units of the metric system for mass include:

• extbf{Gram (g)}: The fundamental unit of mass.
• extbf{Decigram (dg)}: 1/10 of a gram.
• extbf{Kilogram (kg)}: 1000 grams.

By using the metric system's base-ten structure, converting between units becomes straightforward. For mass, each step up or down the scale involves multiplying or dividing by powers of ten. This regularity makes it simple to understand and use, enhancing clarity in problems involving weight comparison and mass conversion.

Mass Conversion

Mass conversion involves changing a measurement from one unit to another, often to make comparisons easier, as in our exercise example. Understanding mass conversion is key to interpreting and solving such problems.
For converting between units in the metric system, remember:

• extbf{To convert from smaller to larger units (e.g., from grams to kilograms), divide by a power of ten.} Example: \(1000 \text{ g} \div 1000 = 1 \text{ kg}\).
• extbf{To convert from larger to smaller units (e.g., from kilograms to grams), multiply by a power of ten.} Example: \(1 \text{ kg} \times 1000 = 1000 \text{ g}\).

In our problem, converting 1 decigram (0.1 grams) and 1 kilogram (1000 grams) into grams allowed for a direct comparison, reinforcing the concept that 1000 grams is much heavier than 0.1 grams. Always keep conversion factors handy, as they ensure precision and help avoid confusion in calculations.