Use metric conversion factors to solve each of the following problems:
b. A glass of orange juice contains 3.2 dL of juice. How many milliliters of orange juice are in the glass?

Verified step by step guidance

1. Identify the given quantity and its unit: The problem states that the glass contains 3.2 dL of orange juice. The goal is to convert this into milliliters (mL).
2. Recall the metric conversion factor between deciliters (dL) and milliliters (mL): 1 dL = 100 mL.
3. Set up the conversion equation using the conversion factor. Multiply the given quantity (3.2 dL) by the conversion factor (100 mL/1 dL). This ensures the dL units cancel out, leaving the result in mL.
4. Write the equation in MathML format: $3.2\times 100/1$
5. Perform the multiplication to find the number of milliliters. The final result will be expressed in mL.

Key Concepts

Metric Units

The metric system is a decimal-based system of measurement used globally, which includes units such as liters (L), deciliters (dL), and milliliters (mL). Understanding these units is essential for converting between them, as they are based on powers of ten, making calculations straightforward.

Conversion Factors

Conversion factors are ratios that express how many of one unit are equal to another unit. For example, 1 dL is equal to 100 mL. Using conversion factors allows for the transformation of measurements from one unit to another, which is crucial for solving problems involving different metric units.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert between units by multiplying by conversion factors. This method ensures that units cancel appropriately, leading to the desired unit in the final answer. It is a systematic approach that helps verify the correctness of unit conversions.