Are you curious to know what is an exact number? You have come to the right place as I am going to tell you everything about an exact number in a very simple explanation. Without further discussion let’s begin to know what is an exact number?
What Is An Exact Number?
In mathematics, an exact number is a value that is known precisely, without any error or uncertainty. Exact numbers are important because they form the foundation of many mathematical concepts and calculations, and they are often used in scientific and engineering applications where precision is crucial.
Examples of exact numbers include integers, fractions, and irrational numbers such as pi or the square root of 2. These values are exact because they can be defined precisely and their values are not subject to any measurement or approximation.
Integers, for example, are exact numbers because they are whole numbers that can be counted without any error or uncertainty. Similarly, fractions are exact numbers because they can be expressed as a ratio of two integers, and their values are known exactly. For example, the fraction 1/3 represents exactly one-third of a whole, and the fraction 2/7 represents exactly two-sevenths of a whole.
Irrational numbers, on the other hand, are numbers that cannot be expressed as a simple fraction, but their values are still known exactly. For example, the value of pi is an irrational number that represents the ratio of the circumference of a circle to its diameter, and its value is known to an infinite number of decimal places. Similarly, the square root of 2 is an irrational number that represents the length of the diagonal of a square with sides of length 1, and its value is also known to an infinite number of decimal places.
In contrast, approximate numbers are values that are subject to some degree of error or uncertainty. For example, if you measure the length of a table with a ruler, your measurement will be subject to some degree of error due to limitations in the accuracy of the ruler and your ability to read it. Similarly, if you calculate the value of a mathematical expression using a calculator or a computer program, your answer will be subject to some degree of rounding error due to the limitations of the numerical representation used by the calculator or computer.
In conclusion, exact numbers are an essential concept in mathematics and science, as they allow us to work with values that are known precisely and without any error or uncertainty. Whether you are calculating the circumference of a circle, measuring the volume of a liquid, or designing a bridge, the ability to work with exact numbers is essential for achieving accurate and reliable results.
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FAQ
What Is An Example Of An Exact Number?
An exact number is a value that is known with complete certainty. Examples of exact numbers are counted numbers of objects or certain unit conversions. For example, there are exactly 3 feet in 1 yard. There are exactly 12 eggs in a dozen.
How Do You Know If A Number Is Exact?
Exact numbers have no uncertainty. You can think of them as having an infinite number of significant digits. This is not possible for any measurement, but it is possible in these cases: Counted items.
Is 2.54 Cm An Exact Number?
- Conversions between English and Metric systems are generally NOT exact. Exceptions will be pointed out to you. e.g. 1 in = 2.54 cm exactly (1 and 2.54 are both exact.)
What Are Exact And Non-Exact Numbers?
Exact and inexact numbers.
An exact number has a value that has no uncertainty associated with it. Exact numbers occur in definitions, in counting, and in simple fractions. An inexact number has a value that has a degree of uncertainty associated with it. Inexact numbers are generated anytime a measurement is made.
Is 273.15 An Exact Number?
The Kelvin and the degree Celsius are the same sizes. Note that 273.15 is an exact number.
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