Use metric conversion factors to solve each of the following problems:
d. A jar contains 0.29 kg of olives. How many grams of olives are in the jar?

Verified step by step guidance

1. Step 1: Identify the given quantity and the desired unit. The given quantity is 0.29 kg, and the desired unit is grams (g).
2. Step 2: Recall the metric conversion factor between kilograms and grams. 1 kilogram (kg) is equal to 1000 grams (g).
3. Step 3: Set up the conversion equation using the conversion factor. Multiply the given quantity (0.29 kg) by the conversion factor (1000 g/kg). The equation is: $0.29\times 1000$.
4. Step 4: Ensure that the units cancel appropriately. Kilograms (kg) in the numerator and denominator cancel out, leaving grams (g) as the final unit.
5. Step 5: Perform the multiplication to find the number of grams. The result will be expressed in grams (g).

Key Concepts

Metric System

The metric system is a decimal-based system of measurement used globally, which includes units such as meters for length, liters for volume, and grams for mass. It is based on powers of ten, making conversions straightforward. Understanding the metric system is essential for accurately converting between different units, such as kilograms and grams.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. This involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. For example, to convert kilograms to grams, one must know that 1 kg equals 1000 grams, allowing for easy calculation.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert between units by multiplying by conversion factors. It ensures that the units cancel appropriately, leading to the desired unit in the final answer. This method is particularly useful in solving problems involving different measurement systems, ensuring accuracy in calculations.