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Chapter 1: Problem 19

Give examples of two numbers, one that is exact (no uncertainty) and one that is not, by using them in a sentence.

Short Answer

Expert verified
An exact number is '12,' as in "There are exactly 12 months in a year." A non-exact number is 'about 5,000,' as in "The stadium can hold about 5,000 spectators."

Step by step solution

01

Identify an Exact Number

An exact number is one that is known with complete certainty. For example, "A dozen" always means exactly 12. Therefore, '12' is an exact number.
02

Identify a Non-Exact Number

A non-exact number is one that has some degree of uncertainty or estimation. For instance, saying "approximately 5,000 people attended the concert" implies that the number 5,000 is an estimate and there is uncertainty involved.
03

Create a Sentence with Exact Number

After identifying '12' as an exact number, a sentence can be: "There are exactly 12 months in a year." Here, '12' is known without any estimation or uncertainty.
04

Create a Sentence with Non-Exact Number

For the non-exact number identified as '5,000,' a possible sentence is: "The stadium can hold about 5,000 spectators." Here, 'about 5,000' suggests that the number is not precise and could vary.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exact Numbers
Exact numbers have no uncertainty; they are numbers known with complete assurance. These numbers usually result from definitions or counts, such as the number of items in a dozen, which is always 12. Since exact numbers are certain, they do not produce any ambiguity and are not subject to estimation or variability.
Common examples of exact numbers include:
  • Counted items: The presence of 3 apples in a basket is exact.
  • Defined quantities: There are exactly 60 minutes in an hour.
  • Mathematical constants: In geometry, a square always has 4 sides.
Using exact numbers in calculations keeps results precise as they do not contribute additional uncertainty.
Non-Exact Numbers
Non-exact numbers, unlike exact numbers, carry some degree of uncertainty. They usually arise in contexts where approximation or estimation is necessary, such as in measurements or predictions. Non-exact numbers are typically associated with real-world scenarios where obtaining a perfectly precise value isn't possible or practical.
Instances where non-exact numbers are used include:
  • Estimates: Approximately 20 people attended the meeting.
  • Measurements: A length measured as 15.8 cm could vary slightly.
  • Averages: The average score of the class was around 75%.
Recognizing whether a number is non-exact is important in analysis because it affects how we interpret results and make decisions based on those figures.
Estimation in Measurements
Estimation plays a crucial role in the world of measurements, especially when achieving accuracy isn't feasible. This often leads to the usage of non-exact numbers, which include an inherent level of approximation. Estimations help provide a working number that is sufficiently close to a real value, making it useful for practical applications.

Estimation can be seen in:
  • Scientific measurements: Estimating the weight of a car at about 1500 kg when precise weighing isn't possible.
  • Everyday life: Guessing it takes around 20 minutes to get to a location during traffic.
  • Construction and engineering: Estimating building costs at approximately $200 per square foot.
Although estimations can never entirely be free of error, understanding estimation's role and factoring in its limitations is essential for effective measurement and analysis.

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