Question

Indicate if each of the following is answered with an exact number or a measured number: a. number of legs b. height of table c. number of chairs at the table d. area of tabletop

Short answer

Exact: number of legs, number of chairs at the table; Measured: height of table, area of tabletop.

Step-by-step solution

- Number of Legs

Determine whether 'number of legs' is an exact or measured number. An exact number is a countable number without any uncertainty. Since legs can be counted precisely, 'number of legs' is an exact number.

- Height of Table

Determine whether 'height of table' is an exact or measured number. Measurements involving dimensions or other quantities subject to variation and precision are considered measured numbers. Since the height of a table requires measurement, it is a measured number.

- Number of Chairs at the Table

Determine whether 'number of chairs at the table' is an exact or measured number. Similar to the number of legs, 'number of chairs at the table' can be counted without any ambiguity, making it an exact number.

- Area of Tabletop

Determine whether 'area of tabletop' is an exact or measured number. Calculating the area involves measurements of length and width, which are subject to measuring precision. Thus, 'area of tabletop' is a measured number.

Key concepts

exact number

An exact number is a countable number without any uncertainty. Exact numbers include quantities that can be counted precisely, like the number of students in a classroom or the number of fingers on your hand. These numbers do not involve any estimation or measurement errors.
The following aspects clarify exact numbers:

• Exact numbers are integers, meaning they are whole numbers without fractions or decimals.
• The precision is absolute, as there is no room for ambiguity or error while counting these values.

In our exercise, examples of exact numbers are 'number of legs' and 'number of chairs at the table'. These can be physically counted, ensuring exactitude and clarity without any inaccuracy or approximation.

measured number

A measured number is obtained when a quantity is measured rather than counted. Measurements involve some level of error or uncertainty because they depend on the precision of the measuring instrument used.
Here are some key characteristics of measured numbers:

• Measured numbers often contain decimal points or fractions.
• The precision and accuracy of these numbers can vary due to instrument calibration, human error, or environmental factors.

In the exercise, examples of measured numbers include the 'height of the table' and the 'area of the tabletop'. These quantities require measurement and are not exact due to potential inaccuracies and limitations in measuring tools.

measurement precision

Measurement precision refers to how close repeated measurements are to each other. Precision is crucial for ensuring that measured numbers are reliable and accurate.
Important points to consider about measurement precision include:

• Precision is different from accuracy; precision measures how consistent the results are, while accuracy measures how close the results are to the true value.
• High precision requires sophisticated instruments and techniques to reduce random errors.

For instance, when measuring the height of a table, using a tape measure might yield a different result each time due to slight variations in where and how the measurement is taken. Higher precision can be achieved with more accurate tools like laser distance measurers.

countable number

A countable number refers to quantities that can be directly counted rather than measured. Countable numbers are inherently exact because they do not involve measurement uncertainty.
Notable aspects of countable numbers are:

• Countable numbers are strictly integers, meaning they are whole without any fractions.
• These numbers remain consistent regardless of counting method or occurrence.

Examples from our exercise include 'number of legs' and 'number of chairs at the table'. These quantities can be counted directly, thus being exact and free from any variation or error typical of measurements.