Problem 27 - Chemistry and Chemical Reactivity

Question

A book has a mass of \(2.52 \mathrm{kg} .\) What is this mass in grams?

Step-by-Step Solution

Answer

The mass of the book is 2520 grams.

Step 1: Understand the Units

The problem is asking to convert the mass of the book from kilograms (kg) to grams (g). We know that the relationship between kilograms and grams is that 1 kilogram is equivalent to 1000 grams.

Step 2: Set Up the Conversion

Given: Mass of the book = 2.52 kg. We need to convert this mass to grams. To do this, we will multiply the mass in kilograms by the conversion factor of 1000 grams per kilogram.

Step 3: Perform the Calculation

Multiply the given mass in kilograms by the conversion factor: \[ 2.52 ext{ kg} imes 1000 ext{ g/kg} = 2520 ext{ g} \] So, the mass of the book in grams is 2520 grams.

Step 4: Verify the Result

Check the calculation to ensure no steps were missed and the conversion factor applied correctly. Everything checks out: multiplying 2.52 by 1000 results in 2520.

Key Concepts

mass conversion

Mass conversion is a fundamental concept in science and everyday life. It involves changing a measurement of mass from one unit to another, which is important when working with different measurement systems or simply when you need more precision.

• Mass conversion ensures accuracy. When measuring substances, especially in cooking or chemistry, using the right unit is essential.
• It requires a clear understanding of the relationship between different units of mass.
• Converting mass allows you to compare different objects or substances that may be measured in different units.

A common scenario is converting between units within the metric system, such as kilograms to grams. Having a solid grasp on how to convert mass can help in various fields such as physics, engineering, and even in daily tasks, like determining postal shipping costs.

kilograms to grams

Converting kilograms to grams is a straightforward and commonly needed conversion within the metric system. This conversion is often used because kilograms and grams are standard metric units for mass, with grams being suited for smaller objects and kilograms for larger ones.
To convert:

• Recall that 1 kilogram is equal to 1000 grams.
• Therefore, to convert any mass from kilograms to grams, multiply the mass in kilograms by 1000.

For example, if an object has a mass of 2.52 kilograms, multiplying by 1000 gives:\[2.52 ext{ kg} imes 1000 ext{ g/kg} = 2520 ext{ g}\] This simple conversion demonstrates how larger units of mass can be expressed as smaller units, providing finer granularity in measurement. Converting kilograms to grams is a useful skill in science classes, especially when conducting experiments that require precise measurements.

metric system conversion

The metric system is a decimal-based system of measurement used around the world. It is designed to be simple and logical, making conversions between units straightforward.

• The system is based on standards such as meters, kilograms, and liters, each subdivided into units by powers of ten.
• Converting within the metric system typically involves multiplying or dividing by 10, 100, 1,000, etc.

When dealing with metric system conversion, it helps to remember the prefixes:

• Kilo-, which means multiply by 1,000.
• Cent-, meaning multiply by 0.01.
• Milli-, meaning multiply by 0.001.

An example conversion is between kilograms to grams, where you multiply by 1,000 to scale down from a larger unit to a smaller one. This consistent usage of powers of ten makes converting units like mass, length, or volume intuitive, especially useful in science and engineering.