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Is 3.14 a non-terminating decimal?

Yes, 3.14 is a non-terminating decimal. A non-terminating decimal is a decimal number that has digits that go on forever without a pattern or repeating sequence. The decimal representation of 3.14 is infinite, and it does not terminate or end at any point. It continues indefinitely, with no discernible pattern or repetition.

To illustrate this point, we can represent 3.14 as a fraction, which would be 314/100. When we simplify this fraction, we get 157/50. This shows us that 3.14 is equal to a fraction with a numerator and denominator, both of which are integers. However, when we convert this fraction to a decimal, we get 3.14 again. This shows us that the decimal representation of 3.14 is non-terminating and has an infinite number of decimal places.

3.14 is a non-terminating decimal because it has an endless number of decimal places, with no discernible pattern or repetition. It is an important mathematical constant used in many fields, including geometry, trigonometry, and calculus, and it plays a crucial role in understanding the properties of circles and other geometric shapes.

What is an example of a non-terminating rational number?

A non-terminating rational number is a rational number that goes on forever after the decimal point, without repeating any pattern. An example of a non-terminating rational number is 1/3. When we divide 1 by 3, we get the decimal 0.3333…, which goes on forever without ever ending or repeating. Another example of a non-terminating rational number is 2/7. When we divide 2 by 7, we get the decimal 0.2857142857…, which also goes on forever without any repeating pattern.

There are other examples of non-terminating rational numbers, such as 7/12, 5/11, and 73/137. These numbers all have decimals that go on forever, with no repeating pattern. Non-terminating rational numbers are interesting because they show that there are some numbers that can’t be represented exactly by a fraction, but are still rational numbers, because they can be expressed as a ratio of two integers.

In contrast, terminating rational numbers are rational numbers that have a finite number of decimal places, such as 1/2 (which has the decimal representation 0.5) or 3/4 (which has the decimal representation 0.75). Terminating rational numbers are easy to work with, because they can be easily converted to fractions. However, non-terminating rational numbers are more challenging, because they cannot be represented exactly by a finite number of digits, and require special notations or representations to be worked with accurately.