Question

Which weighs more, \(100 \mathrm{g}\) of water or \(1 \mathrm{kg}\) of water?

Short answer

1 kilogram of water weighs more than 100 grams of water because 1 kilogram is equal to 1000 grams, and 1000 grams is greater than 100 grams.

Step-by-step solution

Understand the units of mass

Both grams and kilograms are units of mass. We can use these units to measure the amount of water given in the problem. We need to understand the relationship between these units to be able to compare them. 1 kilogram (kg) is equal to 1000 grams (g). So, when comparing measurements in grams and kilograms, we will keep this conversion in mind.

Convert units if necessary

In this problem, we have 100 grams of water and 1 kilogram of water. We need to convert the kilogram unit to grams or vice versa to make the comparison possible. Since it's easier to convert kilograms to grams, we'll do that: 1 kilogram of water = 1000 grams of water Now we have: - 100 grams of water - 1 kilogram of water = 1000 grams of water

Compare the weights of the two amounts of water

Now that we have both amounts of water in the same unit (grams), we can compare them. - 100 grams of water - 1000 grams of water Since 1000 grams is greater than 100 grams, it is clear that 1 kilogram (or 1000 grams) of water weighs more than 100 grams of water.

Key concepts

Mass Units

Mass is a fundamental quantity in physics that measures the amount of matter in an object. It is essential to comprehend the different mass units used in everyday measurements. Two common units of mass are grams and kilograms.
Grams and kilograms are part of the metric system, which is widely used around the world for scientific and everyday measurements. The metric system is preferred for its simplicity and ease of conversion between units.

• Gram (g): A gram is a basic unit of mass in the metric system. It is often used to weigh lighter items such as small packages or ingredients for cooking.
• Kilogram (kg): A kilogram is the base unit of mass in the International System of Units (SI). It is equal to 1000 grams and is commonly used for measuring mass when dealing with larger quantities of material or items, such as body weights or packages.

Gram to Kilogram Conversion

Converting between grams and kilograms is a straightforward process due to the metric system's design. Understanding this conversion is essential in science and daily life for accurate measurements.
A major advantage of the metric system is that units scale by powers of ten. For mass, the conversion factor between grams and kilograms is 1000. This means:

• 1 kilogram (kg) = 1000 grams (g)
• 1 gram (g) = 0.001 kilograms (kg)

When converting from grams to kilograms, divide the number of grams by 1000. Conversely, to convert kilograms to grams, multiply the number of kilograms by 1000.
For example, converting 500 grams to kilograms involves dividing by 1000: \[500 \, \text{g} = \frac{500}{1000} = 0.5 \, \text{kg}\]

Comparison of Weights

Comparing weights is a critical skill for analyzing and solving problems related to mass. To accurately compare weights, all quantities must use the same unit of measurement.
In our example problem, we are comparing 100 grams of water and 1 kilogram of water. To make a sound comparison, it's beneficial to convert all measurements to a single unit.
Upon converting 1 kilogram of water to grams, we have:

• 1 kilogram of water = 1000 grams
• 100 grams of water = 100 grams

Now, with both quantities in grams, it is clear that 1000 grams (1 kilogram) is greater than 100 grams. Thus, 1 kilogram of water weighs more than 100 grams of water.
This process highlights the simplicity and necessity of unit conversion for accurate comparisons in both educational settings and real-life scenarios.