The number 3.142857142857 is a rational number. A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In the case of 3.142857142857, it can be expressed as the ratio of the integers 22 and 7, i.e., 22/7. Therefore, it is a rational number.
The number 3.142857142857 is actually a recurring decimal, which means that it has a repeating pattern of digits after the decimal point. In this case, the repeating pattern is “142857,” which repeats infinitely. However, even though the decimal representation of the number has an infinite series of digits, it can still be expressed as a finite ratio of two integers, making it a rational number.
In contrast, an irrational number is a number that cannot be expressed as a ratio of two integers. Examples of irrational numbers include pi (π) and the square root of 2. These numbers have decimal representations that go on infinitely without any repeating pattern of digits.
3.142857142857 is a rational number since it can be expressed as a ratio of two integers, namely 22 and 7. Although it is a recurring decimal, the fact that it can be expressed in this way means that it is not an irrational number.
Is 5.676677666777 a rational number?
In order to determine whether 5.676677666777 is a rational number 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.
Therefore, to check whether 5.676677666777 is a rational number, we need to check whether it can be expressed as a ratio of two integers. We can do this by converting the decimal 5.676677666777 into a fraction form. To do this, we can count the number of decimal places after the decimal point and multiply the number by a power of ten.
In this case, we have 12 decimal places after the decimal point so we can multiply the number by 10^12. This gives us:
5.676677666777 x 10^12 = 5676677666777
Now, we can see that 5676677666777 is indeed an integer number. Therefore, we can express 5.676677666777 as the ratio of 5676677666777 to 10^12, which are both integers. This means that 5.676677666777 is indeed a rational number.
5.676677666777 is a rational number because it can be expressed as a ratio of two integers, namely 5676677666777 and 10^12.
Is 3.141141114 an irrational number True or false?
The number 3.141141114 is a decimal with an infinitely repeating pattern of “14114”. To determine whether it is irrational, we must first define what an irrational number is. An irrational number is a number that cannot be expressed as a finite or repeating decimal. Since 3.141141114 has a repeating decimal pattern, it is a rational number.
The statement “3.141141114 is an irrational number” is false.
Is 9.293847210103938 a rational number?
A rational number is defined as any number that can be expressed as a ratio of two integers. In other words, if we can write the number as a fraction of two integers, then it is a rational number.
By looking at the given number 9.293847210103938, we can see that it is a decimal number with no repeating pattern. However, we can convert this number into a fraction and see if it satisfies the definition of a rational number.
To convert the given decimal into a fraction, we need to count the number of decimal places and write the number over a power of 10. In this case, there are 15 decimal places, so we can write the number as:
9.293847210103938 = 9293847210103938/10^15
Now, we need to simplify the fraction by dividing both the numerator and the denominator by their greatest common factor. In this case, the greatest common factor is 2. So, we get:
9293847210103938/10^15 = 4646923605051969/5^15
Since we have expressed the given number as a ratio of two integers, and simplified it to its lowest form, we can conclude that 9.293847210103938 is indeed a rational number.
Is 43.123456789 they are rational or not?
A rational number is a number that can be expressed as a finite or repeating decimal. An irrational number, on the other hand, is a number that cannot be expressed as a fraction and has an infinite non-repeating decimal representation.
In the case of 43.123456789, we can see that it is a finite decimal. Therefore, it is a rational number. To prove this, we can convert 43.123456789 into a fraction using place value notation.
43.123456789 can be written as:
43 + 0.1 + 0.02 + 0.003 + 0.0004 + 0.00005 + 0.000006 + 0.0000007 + 0.00000008 + 0.000000009
To express this as a fraction, we can write:
43 + 1/10 + 2/100 + 3/1000 + 4/10000 + 5/100000 + 6/1000000 + 7/10000000 + 8/100000000 + 9/1000000000
We can then combine the fractions to get:
(43 * 10000000000 + 123456789)/1000000000
Simplifying this gives us:
43123456789/1000000000
This is a fraction in its lowest terms and can be expressed as the ratio of two integers. Therefore, 43.123456789 is a rational number.