Question

Convert the following to the equivalent measures indicated. \(82 \mathrm{~kg}=\) ______ \(\mathrm{g}\)

Short answer

82 kg is equivalent to 82000 grams.

Step-by-step solution

Understanding the Conversion Relationship

To convert kilograms to grams, you need to understand that 1 kilogram equals 1000 grams. This is the basic conversion factor you will use.

Setting Up the Conversion Equation

Set up the conversion using the relation: \[ \text{grams} = \text{kilograms} \times 1000 \]. Here, you will replace 'kilograms' with the given value, 82 kg.

Performing the Calculation

Substitute the 82 kg into the equation: \[ \text{grams} = 82 \times 1000 \].

Calculating the Result

Calculate the product: \[ 82 \times 1000 = 82000 \]. This means 82 kg is equal to 82000 grams.

Key concepts

Kilograms to Grams

Unit conversion involves changing the measurement of a quantity from one unit to another while retaining its original value. For the conversion from kilograms to grams, it's essential to understand the relationship between these two units of mass. The kilogram is a base unit in the metric system, and one kilogram is equal to 1000 grams. This means if you have 1 kilogram, you essentially have 1000 grams. This relationship is crucial when performing calculations involving these units, as it serves as the fundamental basis for the conversion.

Conversion Factor

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. In our case, the conversion from kilograms to grams uses a conversion factor of 1000.
This means:

• You multiply the number of kilograms by 1000 to get the equivalent number in grams.
• The factor of 1000 is derived from the fact that there are 1000 grams in a kilogram.

Understanding and applying conversion factors is essential for accurate and efficient unit conversions. They ensure that your calculations convert units correctly and that the resulting measurements retain the same relative value.

Calculation Process

The calculation process for converting units like kilograms to grams follows a simple multiplication equation. This multi-step approach ensures accuracy and clarity:
First, identify the number of kilograms you need to convert. In this instance, it's 82 kg.
Next, use the conversion factor of 1000 grams per kilogram in the following formula:\[\text{grams} = \text{kilograms} \times 1000\]Thus, substitute the given value into the equation:\[\text{grams} = 82 \times 1000\]This straightforward calculation results in the conversion of 82 kg into grams. Remember, this step-by-step procedure helps eliminate confusion and mistakes.

Mathematical Equations

Mathematical equations are formulas that express relationships between numbers and variables. In unit conversions, they provide a clear and consistent method for performing calculations. For our example, the equation used is:\[\text{grams} = \text{kilograms} \times 1000\]Equations like these are valuable because:

• They provide a structured approach to solving problems.
• They enable precise and repeatable calculations.

In practical terms, you can see how this mathematical equation takes the given amount in kilograms and effortlessly translates it into grams by applying multiplication. Utilizing equations for conversions ensures accuracy and efficiency, particularly when handling larger numbers or multiple conversions.