Question

Convert the following numbers of calories into kilocalories. a. 8254 cal b. 41.5 cal c. \(8.231 \times 10^{3}\) cal d. 752,900 cal

Short answer

a. 8.254 kcal b. 0.0415 kcal c. 8.231 kcal d. 752.9 kcal

Step-by-step solution

(Step 1: Convert 8254 cal to kcal)

Divide 8254 by 1000: \( 8254 \textrm{ cal} \times \frac{1 \textrm{ kcal}}{1000 \textrm{ cal}} = 8.254 \textrm{ kcal} \) a. The conversion of 8254 cal to kcal is 8.254 kcal.

(Step 2: Convert 41.5 cal to kcal)

Divide 41.5 by 1000: \( 41.5 \textrm{ cal} \times \frac{1 \textrm{ kcal}}{1000 \textrm{ cal}} = 0.0415 \textrm{ kcal} \) b. The conversion of 41.5 cal to kcal is 0.0415 kcal.

(Step 3: Convert \(8.231 \times 10^{3}\) cal to kcal)

Divide \(8.231 \times 10^{3}\) by 1000: \( (8.231 \times 10^{3}) \textrm{ cal} \times \frac{1 \textrm{ kcal}}{1000 \textrm{ cal}} = 8.231 \textrm{ kcal} \) c. The conversion of \(8.231 \times 10^{3}\) cal to kcal is 8.231 kcal.

(Step 4: Convert 752,900 cal to kcal)

Divide 752,900 by 1000: \( 752,900 \textrm{ cal} \times \frac{1 \textrm{ kcal}}{1000 \textrm{ cal}} = 752.9 \textrm{ kcal} \) d. The conversion of 752,900 cal to kcal is 752.9 kcal.

Key concepts

Calories to Kilocalories

Calories, often abbreviated as "cal," are units of energy that are commonly used in food labeling and nutrition. In science and nutrition, we also encounter kilocalories, abbreviated as "kcal." Even though we frequently see terms like "calories" in diet contexts, what is often referred to as a calorie is technically a kilocalorie. This is because a kilocalorie is equivalent to 1,000 calories. For example, when nutrition labels say a snack has 200 calories, it may actually contain 200 kilocalories or 200,000 calories. The conversion from calories to kilocalories is straightforward since there are exactly 1,000 calories in 1 kilocalorie. This makes it easy to convert between the two by simply dividing the number of calories by 1,000. This unit conversion helps maintain consistency in the metric system and makes handling large numbers more manageable. Whether you are studying biology, cooking, or just reading a nutrition label, understanding how to convert between calories and kilocalories is valuable.

Division

Division is a fundamental mathematical operation that can be thought of as the process of distributing a quantity evenly into a specified number of parts. In the context of unit conversion, division plays a key role. When converting calories to kilocalories, as seen in the above examples, you divide the number of calories by 1,000. This is because you are breaking down a large quantity of calories into smaller kilocalorie units.

• Take the total number of calories.
• Divide by 1,000 to convert to kilocalories.

The formula is simple: \( ext{calories} \times \frac{1 \text{ kcal}}{1000 \text{ cal}} = \text{kilocalories} \). This expression shows that for every 1,000 calories, you have a complete kilocalorie. This approach simplifies comparisons and makes calculations easier when interpreting dietary information, conducting experiments, or engaging in physical activities.

Metric System

The metric system is an internationally recognized system for measurements that is based on powers of ten. It simplifies the process of converting between units by using this consistent factor. For instance, converting within the metric system, such as calories to kilocalories, is streamlined because they are related by a factor of 1,000. This method of conversion fits neatly into the broader metric system, where prefixes like "kilo" indicate a multiplication or division by 1,000.

• The base unit in this context is the calorie.
• The kilocalorie is a derivative unit, which is 1,000 times the base unit.

The metric system's reliance on base-10 makes it intuitive and widely adopted in scientific fields, facilitating global communication and understanding. Whether measuring distance, volume, or energy, the metric system's uniform structure allows for seamless conversion and comprehension, thus making it an essential part of scientific and everyday measurement.