Problem 37 - Calculate With Confidence

Question

Convert the following metric measures by moving the decimal. \(8 \mathrm{~kg}=\) ______ \(\mathrm{g}\)

Step-by-Step Solution

Answer

8 kg is equal to 8000 g.

Step 1: Understanding the Conversion Factor

To convert kilograms to grams, we need to remember the basic fact that 1 kilogram is equal to 1000 grams. This is a standard metric conversion.

Step 2: Setting Up the Conversion

We know that 8 kilograms need to be converted to grams. Using the conversion factor, this can be expressed as: 8 kg = 8 kg × 1000 g/kg.

Step 3: Performing the Calculation

Now, we multiply 8 by the conversion factor (1000) to convert kilograms to grams: \[ 8 imes 1000 = 8000 \]

Step 4: Writing the Result

Therefore, 8 kilograms is equal to 8000 grams. You move the decimal point 3 places to the right when converting from kg to g to account for multiplying by 1000.

Key Concepts

kilograms to grams

When dealing with the metric system, one of the most common conversions we encounter is from kilograms to grams. This conversion is essential because it allows us to express weight in smaller, more workable units without changes to the actual quantity. In the metric system, which is based on powers of 10, 1 kilogram is equal to 1000 grams. Hence, to convert a value from kilograms to grams, we multiply the number of kilograms by 1000. For example, converting 8 kilograms to grams using this relationship is straightforward:

• Multiply 8 (kilograms) by 1000 (since 1 kg = 1000 g)
• The result is 8000 grams

This calculation shows that 8 kilograms is equal to 8000 grams, making the process not only simple but also systematic when using the metric system.

conversion factor

A conversion factor is a key concept in changing units within the same system, such as between kilograms and grams. The conversion factor helps to maintain the proportionality of the units, thereby ensuring that the quantity remains consistent, although the units change. In the case of kilograms to grams, our conversion factor is 1000. Here’s how it works:

• Identify the conversion factor: here it is 1000 g/1 kg.
• Use this factor to change kilograms to grams by multiplying the number of kilograms you have by 1000.

Using conversion factors helps avoid mistakes and makes calculations easier by providing a clear path from one unit to another. It's all about maintaining equality; different units, same value.

decimal movement in conversions

While performing metric system conversions, understanding how decimal movement works can be a huge time-saver. When converting from kilograms to grams, we use the conversion factor of 1000, which means we move the decimal point three places to the right. This is because:

• 1000 is equivalent to 10³, representing three decimal shifts.
• For every one step up in units, the decimal shifts one place right.

In our example, 8 kilograms becomes 8000 grams simply by moving the decimal three places to the right. Suppose you have an integer (8 kg) without visible decimals; you can envision it as 8.000 before shifting. After moving the decimal, it changes to 8000, making it intuitive to perform conversions without heavy calculations. In daily practice, this method allows you to adjust unit sizes quickly by focusing on the decimal point's position.