which of the following is an irrational number-1 5/29 0.343434 v2/3 or 87.9821
The irrational number among the options provided is √2/3. Irrational numbers are numbers that cannot be expressed as a fraction of two integers and do not terminate or repeat.
Answer
The irrational number among the options provided is √2/3.
To determine whether each of the given numbers is irrational, we need to recall that an irrational number cannot be expressed as a fraction or a terminating or repeating decimal.
Let's analyze each option:
1. 5/29: This is a fraction, so it is not an irrational number.
2. 0.343434: This decimal repeats the pattern "34," which makes it a repeating decimal. Therefore, it is not an irrational number.
3. √2/3: This is the square root of 2 divided by 3. The square root of 2 is an irrational number, and any division involving an irrational number remains irrational. Therefore, √2/3 is an irrational number.
4. 87.9821: This decimal terminates, so it is not an irrational number.
The only option that is an irrational number is √2/3.
To determine which of the following numbers is irrational, we need to understand what an irrational number is.
An irrational number is a real number that cannot be expressed as a fraction or a ratio of two integers. It is a non-repeating and non-terminating decimal number.
Let's analyze each of the given numbers:
1. 1: This is a rational number since it can be expressed as 1/1 or any other fraction with 1 as both the numerator and the denominator.
2. 5/29: This is a rational number since it can be expressed as a fraction.
3. 0.343434: This number repeats the pattern "34" indefinitely. It is rational because it can be expressed as 34/99 or any other fraction where the numerator is the repeating digits and the denominator is a multiple of 9.
4. √2/3: The square root of 2 (√2) is an irrational number because it cannot be expressed as a fraction. Dividing it by 3 gives us an irrational number.
5. 87.9821: This number can be expressed as a terminating decimal, which means it has a definite end. Therefore, it is a rational number.
From the given options, the number √2/3 is the only irrational number, while the rest are rational numbers.