Identify the exact number(s), if any, in each of the following pairs of numbers:
a. 5 pizzas and 50.0 g of cheese

Verified step by step guidance

1. Step 1: Understand the concept of exact numbers. Exact numbers are values that are counted or defined, not measured. They have no uncertainty and are considered to have an infinite number of significant figures.
2. Step 2: Analyze the first number in the pair, '5 pizzas.' Since this is a counted quantity (you can count the number of pizzas), it is an exact number.
3. Step 3: Analyze the second number in the pair, '50.0 g of cheese.' This is a measured quantity because it involves a unit (grams) and is determined using a measuring device. Measured quantities are not exact and have a limited number of significant figures.
4. Step 4: Conclude that in this pair, '5 pizzas' is the exact number, while '50.0 g of cheese' is a measured number.
5. Step 5: Remember that exact numbers are often integers from counting or defined values (e.g., 1 dozen = 12), while measured numbers involve units and are subject to uncertainty.

Key Concepts

Quantitative Comparison

Quantitative comparison involves evaluating the numerical values of different items to determine their relationships. In this case, it requires assessing the quantities of pizzas and cheese to identify any exact numerical relationships or conversions between them.

Units of Measurement

Units of measurement are standard quantities used to express physical quantities. Understanding the units involved, such as 'pizzas' and 'grams,' is crucial for making accurate comparisons and conversions, as they represent different types of items and quantities.

Conversion Factors

Conversion factors are ratios used to convert one unit of measurement into another. In this scenario, if a specific relationship or conversion between pizzas and grams of cheese exists (e.g., how much cheese is needed per pizza), applying the correct conversion factor is essential for determining the exact numbers.