Problem 46 - Calculate With Confidence

Question

Convert the following metric measures by moving the decimal. \(400 \mathrm{~g}=\) ______ \(\mathrm{kg}\)

Step-by-Step Solution

Answer

400 g = 0.4 kg.

Step 1: Understand Metric Conversion

You need to convert grams (g) to kilograms (kg). In the metric system, 1 kilogram is equal to 1000 grams.

Step 2: Set Up the Conversion

To convert grams to kilograms, you need to divide the number of grams by 1000, because 1 kg = 1000 g. This is equivalent to moving the decimal point three places to the left.

Step 3: Move the Decimal

Start with 400 grams. Move the decimal point three places to the left: 400.0 -> 40.0 -> 4.0 -> 0.4. So, 400 grams is equal to 0.4 kilograms.

Key Concepts

Unit Conversion

Unit conversion is the process of changing a measurement from one unit to another. It is particularly important in fields like science, engineering, and everyday life when measurements need to be standardized or compared. In this exercise, we focus on converting grams (g) to kilograms (kg). In general, when you're performing a unit conversion:

• Identify the equivalencies between the units. For example, 1 kilogram equals 1000 grams.
• Determine the mathematical operation needed to make the conversion. In this case, because there are 1000 grams in a kilogram, you will divide by 1000 to change grams to kilograms.

With these simple steps you can easily convert between units within the metric system by simply adjusting the quantity according to the conversion factor.

Metric System

The metric system is a decimal-based system of measurement used worldwide due to its simplicity and ease of use. It includes units such as meters for length, liters for volume, and grams for mass. The metric system is based on powers of ten, making it extremely straightforward for conversions. For instance, to go from grams to kilograms, you use the metric relation where 1 kilogram equals 1000 grams. This directly implies a factor of 10³. By understanding and recognizing these relationships, you can convert units effortlessly by applying multiplication or division.
Here's why the metric system is favored:

• Simplicity: Based solely on powers of ten, making it easy to multiply or divide.
• Consistency: Widely used globally which standardizes measurements across various fields.
• Universality: Common scientists and educators support it, enhancing cooperation and understanding.

Decimal Point Movement

Decimal point movement is a technique used frequently in the metric system for converting units. When you divide by 10, 100, or 1000, you adjust the decimal point to the left by one, two, or three places, respectively. This technique is particularly useful when converting metric units because the system is based on powers of ten. In the original problem, you need to move the decimal to convert from grams to kilograms. Here's how it works:

• Start with the number you have, which is 400 grams.
• Since 1 kilogram = 1000 grams, move the decimal point three places to the left: 400.0 -> 40.0 -> 4.0 -> 0.4.
• This transformation shows that 400 grams is equivalent to 0.4 kilograms.

Remember, the direction in which you move the decimal point depends on whether you are converting to a larger or smaller unit. Moving left makes the number smaller, which aligns with converting to larger units like kilograms.