Problem 34 - Elementary Algebra

Question

Evaluate \(12 \mathrm{~kg}+54 \mathrm{~g}\). Write the answer in kilograms.

Step-by-Step Solution

Answer

12.054 kg

Step 1: Convert grams to kilograms

First, convert the grams into kilograms. We know that 1 kilogram is equivalent to 1000 grams. Thus, 54 grams is converted to kilograms by dividing by 1000: \[54 \text{ g} = \frac{54}{1000} \text{ kg} = 0.054 \text{ kg} \]

Step 2: Add the weights together

Now, add the converted weight (0.054 kg) to the given weight in kilograms (12 kg). \[12 \text{ kg} + 0.054 \text{ kg} = 12.054 \text{ kg} \]

Key Concepts

Understanding Kilograms

Kilograms (kg) are a standard unit of mass in the metric system. They are commonly used around the world to measure weight. The term 'kilogram' comes from the Greek words 'kilo' meaning a thousand, and 'gram' meaning a small unit of mass. Thus, a kilogram is one thousand grams. Whenever you see an object weighed in kilograms, you're essentially saying that the mass is a certain number of thousands of grams.
For example, if an apple weighs 0.2 kg, it means it weighs 200 grams. Kilograms are very practical, especially when dealing with heavier objects or in contexts where precision is not as crucial, as they simplify large numbers into more manageable figures. Always remember that because a kilogram is 1000 grams, converting between these two units is straightforward by either multiplying or dividing by 1000.

Understanding Grams

Grams (g) are another unit of mass used in the metric system. They are much smaller than kilograms and are often used for lighter objects. One gram is defined as one-thousandth of a kilogram. This means that 1000 grams make up one kilogram. The gram is handy when you need more precision in measurement or when dealing with lighter objects like spices, ingredients in recipes, or small quantities of substances.
Conversion between grams and kilograms is easy because of the base-10 structure of the metric system. To convert grams to kilograms, you divide the number of grams by 1000. For example, to convert 500 grams to kilograms, you'd calculate 500 ÷ 1000 = 0.5 kg. Conversely, to convert kilograms to grams, you simply multiply by 1000. Grams help provide a granular measurement, which is especially useful in scientific experiments and cooking.

Adding Weights: Combining Kilograms and Grams

Adding weights that are expressed in different units—like kilograms and grams—requires a simple conversion for consistency. As shown in the given exercise, start by converting all weights into the same unit. For instance, to add 12 kg and 54 g, begin by converting grams to kilograms:

• 54 grams = 0.054 kilograms (since 1 kg = 1000 g)

Once converted, add both weights that are now in kilograms:

• 12 kg + 0.054 kg = 12.054 kg

This method ensures accuracy and avoids confusion. Always double-check your conversions and calculations for precision.
This process is useful in many practical situations, whether you're mixing ingredients, measuring materials for a project, or just understanding combined weights in recipes. Proper unit conversion makes arithmetic operations with different weight measurements seamless and correct.