# Is 3.31662479036 rational or irrational?

The number 3.31662479036 can be simplified as a fraction by expressing it as the numerator of a fraction and the denominator as 1 followed by the same number of decimal places as the numerator. In this case, the numerator is 331662479036 and the denominator would be 100000000000, giving us the fraction of 331662479036/100000000000.

To determine if this fraction is rational or irrational, we need to first understand what these terms mean. A rational number is any number that can be expressed as the ratio of two integers, meaning it can be written in the form of a/b, where a and b are integers and b is not equal to 0. An irrational number, on the other hand, is any number that cannot be expressed as the ratio of two integers and does not terminate or repeat infinitely.

Since 331662479036 and 100000000000 are both integers, 331662479036/100000000000 is indeed a fraction. However, we are unsure if it can be simplified any further or if it will terminate or repeat.

Using the prime factorization (breaking down) method, we can simplify this fraction by dividing the numerator and denominator by their greatest common factor. In this case, the greatest common factor of the numerator and denominator is 4, so we can simplify the fraction to 82915619759/25000000000.

This fraction can still be simplified further by dividing both the numerator and denominator by 10, resulting in 82915619759/2500000000. Again, both the numerator and denominator are integers, proving that 3.31662479036 is indeed a rational number.

Therefore, in conclusion, we can say that 3.31662479036 is a rational number expressed as the fraction 82915619759/2500000000.

## Is the number 3.24 636363 an integer and irrational number rational number or none of these?

No, the number 3. 24 636363 is neither an integer nor a rational or irrational number. This number is a decimal and cannot be classified as an integer, rational, or irrational number. An integer is any whole number, either negative or positive, whereas rational numbers are any numbers that can be written as a ratio of two integers and irrational numbers are numbers that cannot be written as a simple fraction.

Because the number 3. 24 636363 contains both a non-integer value (3. 24) and a repeating decimal portion (636363), it cannot be classified as an integer, rational, or irrational number.

## Is 1.101001000100001 a rational number?

To determine whether 1.101001000100001 is a rational number or not, we first need to define what a rational number is. A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, a rational number is a number that can be written as a fraction.

Looking at the number 1.101001000100001, we can see that it can be expressed as 11/10 + 1001/10000 + 1/100000 + 1/100000000. However, even though we can write the number as a sum of fractions, it is not necessarily a rational number.

To determine whether it is a rational number or not, we need to look at the decimal expansion of the number. If the decimal expansion is finite or repeating, then the number is rational. If the decimal expansion is non-repeating and non-terminating, then the number is not rational.

In the case of 1.101001000100001, we can see that the decimal expansion is non-repeating and non-terminating. This means the number is not rational. It is what we call an irrational number.

1.101001000100001 is not a rational number. It is an irrational number with a non-repeating and non-terminating decimal expansion.

## Is 0.318564318564318564 rational?

Yes, 0.318564318564318564 is a rational number.

To determine whether a number is rational or not, we need to first understand what a rational number is. A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. This means that a rational number can always be written in the form of p/q, where p and q are integers and q is not equal to zero.

In the case of 0.318564318564318564, we can convert this decimal into a fraction by using place values. The first digit after the decimal point is in the tenths place, the second digit is in the hundredths place, and so on.

Thus, we can write 0.318564318564318564 as 318564318564318564/10^18, since there are 18 digits after the decimal point. 10^18 is simply a way of expressing 1 followed by 18 zeroes.

Now, we can simplify this fraction by dividing both the numerator and denominator by their common factor of 2. This gives us 159282159282159282/5×10^17.

As we can see, this number can be expressed as a ratio of two integers, where the denominator is not equal to zero. Therefore, we can confidently say that 0.318564318564318564 is a rational number.

### Resources

1. How to Find the Square Root of 11? – Cuemath
2. Identifying Rational and Irrational Numbers – Lumen Learning
3. How can you show that 3+ √11 is not a rational number?
4. (1) show that 4 sqrt(2) is an irrational number. (2) prove that 3 …
5. Rational and Irrational Numbers – Fact Monster