Question

Express the quantity of \(3.225 \mathrm{~kJ}\) in calories.

Short answer

3.225 kJ is approximately 771 cal.

Step-by-step solution

Identify the Conversion Factor

To convert energy from kilojoules (kJ) to calories (cal), use the conversion factor: \( 1 \, \text{kJ} = 239.006 \, \text{cal} \).

Set Up the Conversion

Start with the given amount in kilojoules and multiply by the conversion factor to find the equivalent amount in calories. Here, we have \( 3.225 \, \text{kJ} \).

Perform the Calculation

Multiply the kilojoules value by the conversion factor: \( 3.225 \, \text{kJ} \times 239.006 \, \text{cal/kJ} \).

Calculate the Result

Perform the multiplication: \( 3.225 \times 239.006 = 770.792 \). Thus, \( 3.225 \, \text{kJ} = 770.792 \, \text{cal} \).

Rounding the Answer

For simplicity, you can round the calculated result to a reasonable number of significant figures, for instance, rounding to three significant figures gives \( 771 \, \text{cal} \).

Key concepts

kilojoules to calories

When dealing with energy, it's useful to understand how different units convert into one another. Kilojoules and calories are both units of energy used to measure things like food energy or physical activity.
While kilojoules (kJ) are part of the International System of Units (SI), calories (cal) are often used in nutritional contexts.
To express energy accurately, we often need to convert between these two units.

• Kilojoules (kJ) are commonly used worldwide as a measure of energy in food labels.
• Calories are still mainstream in places like the United States for this purpose.

Understanding this conversion is helpful for interpreting food labels and understanding energy information from different sources. This ensures that energy values are quickly and accurately communicated and understood across different systems.

conversion factor

The conversion factor is a crucial element to changing measurements from one unit to another. When converting kilojoules to calories, the conversion factor serves as a bridge between these two units of energy.
In the system of units we're considering, 1 kilojoule is equivalent to 239.006 calories.

• This conversion factor allows you to multiply any kilojoule value by 239.006 to yield an equivalent calorie value.
• It acts as a mathematical tool that simplifies the conversion process.

The reliability of your conversion greatly depends on using the correct factor.
If you use an incorrect factor, your resulting calculation could lead you astray. Therefore, ensuring accuracy here is pivotal to obtaining the correct energy equivalent in calories.

calculation of energy

Performing the calculation of energy conversion involves several steps, each of which ensures precision and clarity.
Once we have the correct conversion factor, we simply multiply the given kilojoules by this factor to obtain the equivalent calorie value.
For instance, if you start with 3.225 kJ, multiplying by the conversion factor gives:\[ 3.225 imes 239.006 = 770.792 \, \text{calories} \]After performing the multiplication, the resulting value can often be rounded for simplicity and practicality, especially if you're looking at a context like food labeling, where precision might be less critical than clarity.
Rounding 770.792 calories to 771 calories makes it more digestible while still maintaining a reasonable degree of accuracy.
Therefore, understanding and executing this conversion properly empowers you to interpret and compare energy values more effectively in everyday contexts.