Identify the exact number(s), if any, in each of the following pairs of numbers:
b. 6 nickels and 16 g of nickel

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, '6 nickels.' Since this is a count of physical objects (nickels), it is an exact number because counting is not subject to measurement uncertainty.
3. Step 3: Analyze the second number, '16 g of nickel.' This is a measured quantity, as it involves the mass of nickel determined using a measuring device. Measured quantities are not exact numbers because they have a degree of uncertainty associated with the measurement.
4. Step 4: Conclude that '6 nickels' is an exact number, while '16 g of nickel' is a measured number.
5. Step 5: Remember that exact numbers are often used in calculations without affecting the number of significant figures, whereas measured numbers require attention to significant figures and uncertainty.

Key Concepts

Units of Measurement

Understanding units of measurement is crucial for comparing quantities. In this question, 'nickels' refers to a count of coins, while 'grams' (g) is a metric unit for mass. Recognizing the difference between these units helps in determining if the quantities can be directly compared or if conversion is necessary.

Nickel as a Material

Nickel is a chemical element and a metal commonly used in coinage. In this context, the question involves both the number of nickel coins (nickels) and the weight of nickel in grams. Knowing that a nickel coin is primarily composed of nickel allows for a better understanding of the relationship between the number of coins and their total mass.

Conversion Between Mass and Quantity

To effectively analyze the question, one must understand how to convert between the mass of a material and the quantity of items made from that material. For example, knowing the weight of a single nickel (approximately 5 grams) allows for the calculation of the total mass of 6 nickels, facilitating a comparison with the 16 grams of nickel.