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Is 0.212121 a rational number?

Yes, 0.212121 is a rational number because it can be expressed as a ratio of two integers. To determine this, we can convert the decimal to a fraction.

Let x = 0.212121

Multiplying both sides by 100, we get:

100x = 21.2121

Subtracting the left sides, we get:

99x = 21

Dividing both sides by 99, we get:

x = 21/99

Therefore, 0.212121 is equal to 21/99 which is a rational number.

How do you know if a number is rational?

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. Therefore, to determine if a number is rational, we need to check whether it can be expressed as a fraction of two integers.

For example, let us consider the number 2.5. This number can be expressed as a ratio of two integers, namely 5 and 2, as 2.5 = 5/2. Hence, 2.5 is a rational number.

Contrarily, if we consider the number pi (π), which is approximately equal to 3.141592654, then it cannot be expressed as a fraction of two integers. Its decimal expansion goes on infinitely, without repeating any group of digits. Therefore, pi is an irrational number.

Another example of an irrational number is the square root of 2 (√2), which is approximately equal to 1.414213562. If we try to express it as a ratio of two integers, we will find that it is impossible. Thus, it is an irrational number.

We can determine whether a number is rational or irrational by checking whether it can be expressed as a ratio of two integers or not. If it can be expressed as such, it is a rational number, and if not, it is an irrational number.

Is this number rational or not?

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. For example, 2/3 is a rational number, since it can be expressed as the ratio of the integers 2 and 3.

To determine if a given number is rational, we need to check if it satisfies this fundamental property. If the number can be expressed as a fraction of two integers, then it is rational. Otherwise, it is irrational.

For example, the number 4 is rational, since it can be expressed as 4/1, which is the ratio of two integers. Similarly, the number 0 is rational, since it can be expressed as 0/1. Irrational numbers, on the other hand, cannot be expressed as a ratio of two integers. Examples of irrational numbers include the square root of 2 (which cannot be expressed as a ratio of two integers) and pi (which cannot be expressed exactly as a decimal or a fraction).

Therefore, to determine whether a given number is rational or not, we need to check if it can be expressed as a fraction of integers. If it can, then it is rational; if not, it is irrational.

Is 0.33333333 terminating or non terminating?

A terminating decimal is a decimal number that has a specific number of digits after the decimal point, meaning that it ends or terminates after a finite number of digits. On the contrary, a non-terminating decimal is a decimal that has an infinite number of digits after the decimal point, which means that it never ends.

In the case of the number 0.33333333, it is a recurring decimal that repeats indefinitely, which means it is a non-terminating decimal. The repeating pattern in this number is the digit 3, which is repeated infinitely. Hence, this number can be represented symbolically as 0.3̅, where the bar over the digit 3 indicates that it repeats infinitely.

Therefore, 0.33333333 is a non-terminating decimal that goes on forever without ending. This decimal representation cannot be simplified to a fraction of two integers, which is a characteristic feature of non-terminating decimals. Lastly, the difference between terminating and non-terminating decimals is an essential concept in mathematics and has various applications in fields such as science, engineering, and economics.

Is 0.33333 a terminating decimal?

No, 0.33333 is not a terminating decimal because a terminating decimal is a decimal number that ends after a finite number of digits. In other words, the decimal has an end point and does not continue indefinitely. 0.33333, however, repeats the number 3 infinitely, thus making it a non-terminating decimal.

It can be expressed as a fraction by placing the repeating 3s in the numerator and the denominator, and simplifying if possible. Therefore, 0.33333 is a repeating decimal, and it can be represented as the fraction 1/3.

What is 0.2222 as a fraction?

0.2222 can be expressed as a fraction by identifying the place value of each digit in the decimal. The first digit after the decimal point is in the tenths place (0.2), the second digit is in the hundredths place (0.02), the third digit is in the thousandths place (0.002), and so on.

To convert 0.2222 into a fraction, we can use the formula:

decimal / 1 = fraction / denominator

Where “fraction” is the numerator of the fraction and “denominator” is the denominator of the fraction.

So, we can start by multiplying both sides of the equation by a power of 10 that moves the decimal point to the right until we have a whole number on the left side. In this case, we can multiply both sides by 10000, since there are four digits after the decimal point:

0.2222 / 1 = fraction / denominator

0.2222 × 10000 / 1 = fraction / denominator × 10000

2222 / 1 = fraction / denominator × 10000

Simplifying the left side, we get:

2222 = fraction / denominator × 10000

Now, we need to find a common factor between the numerator and denominator of the fraction on the right side, in order to simplify it. One common factor between 2222 and 10000 is 2, so we can divide both by 2:

2222 ÷ 2 = 1111

10000 ÷ 2 = 5000

So, the simplified fraction is:

1111 / 5000

Therefore, 0.2222 as a fraction is 1111/5000.