Question

Identify the measured number(s), if any, in each of the following pairs of numbers: a. 3 hamburgers and 6 oz of hamburger b. 1 table and 4 chairs c. \(0.75 \mathrm{lb}\) of grapes and \(350 \mathrm{~g}\) of butter d. \(60 \mathrm{~s}=1 \mathrm{~min}\)

Short answer

Measured numbers are '6 oz of hamburger,' '0.75 lb of grapes,' '350 g of butter,' and '60 s' and '1 min'. Counted numbers are '3 hamburgers,' '1 table,' and '4 chairs'.

Step-by-step solution

Identify Measured and Counted Numbers

A measured number comes from a measurement and has units. A counted number is a number of objects without units.

Pair a: 3 hamburgers and 6 oz of hamburger

The number '3 hamburgers' is a counted number since it counts objects. '6 oz of hamburger' is a measured number since it includes a unit.

Pair b: 1 table and 4 chairs

'1 table' and '4 chairs' are both counted numbers since they count objects without units.

Pair c: 0.75 lb of grapes and 350 g of butter

'0.75 lb of grapes' and '350 g of butter' are both measured numbers since they include units (lb and g).

Pair d: 60 s = 1 min

'60 s' and '1 min' are both measured numbers since they are part of a measurement with units.

Key concepts

Measured Numbers

Measured numbers are values obtained through measuring processes and include units. For example, when you weigh something and get 6 ounces (oz), this value is a measured number because it comes from a measuring tool and includes a unit. Measured numbers are essential in science and daily life to quantify physical quantities accurately.
Examples of measured numbers:

• 6 oz of hamburger
• 0.75 lb of grapes
• 350 g of butter

These numbers help us understand and communicate the magnitude of different quantities, whether we're discussing weight, length, volume, or time.

Counted Numbers

Counted numbers come from counting objects and do not include units. They are complete and exact since they represent a simple tally of items. For instance, if you count 3 hamburgers or 4 chairs, these are counted numbers because they indicate the quantity of individual entities without the involvement of measuring.
Examples of counted numbers:

• 3 hamburgers
• 1 table
• 4 chairs

Unlike measured numbers, counted numbers do not have associated units and are typically whole numbers, representing the discrete count of objects.

Units in Measurements

Units play a crucial role in measurements by providing a scale for the quantities we measure. They are standardized values that help people understand what a number represents. For instance, '20 meters' tells us the length, while '1 kilogram' tells us the mass.
Different units of measurement include:

• Mass: grams (g), kilograms (kg), pounds (lb)
• Length: meters (m), centimeters (cm), feet (ft)
• Volume: liters (L), milliliters (mL), cubic meters (m³)
• Time: seconds (s), minutes (min), hours (h)

Units provide context and meaning to numbers, allowing for clear and precise communication of quantities.

Quantitative Chemistry

Quantitative chemistry focuses on measuring and calculating the quantities of chemical substances. It involves using measured numbers to analyze the composition, reactivity, and properties of materials.
Key aspects of quantitative chemistry include:

• Mass and volume measurements to determine substance quantities.
• Concentration calculations, such as molarity (moles per liter).
• Stoichiometry, which uses measured quantities to predict the results of chemical reactions.

Accurate measurements and appropriate units are essential in quantitative chemistry to ensure that experimental results remain reliable and reproducible.