Question
Which is irrational number _1 5/29, 0.343434, √2/3 or 87.9821
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GPT-4o mini
To determine which of the given numbers is irrational, let's analyze each one:
1. **1 5/29**: This is a mixed number that can be expressed as a fraction (1 + 5/29 = 34/29). Since it can be written as a ratio of two integers, it is a rational number.
2. **0.343434**: This is a repeating decimal (0.343434...) which can also be expressed as a fraction (its exact form would be 34/99). Therefore, it is a rational number.
3. **√2/3**: The square root of 2 (√2) is known to be an irrational number. Dividing an irrational number by a rational number (3, in this case) results in an irrational number. Therefore, √2/3 is irrational.
4. **87.9821**: This is a finite decimal, which can be expressed as a fraction (879821/10000). Thus, it is a rational number.
The only irrational number from the provided choices is **√2/3**.
1. **1 5/29**: This is a mixed number that can be expressed as a fraction (1 + 5/29 = 34/29). Since it can be written as a ratio of two integers, it is a rational number.
2. **0.343434**: This is a repeating decimal (0.343434...) which can also be expressed as a fraction (its exact form would be 34/99). Therefore, it is a rational number.
3. **√2/3**: The square root of 2 (√2) is known to be an irrational number. Dividing an irrational number by a rational number (3, in this case) results in an irrational number. Therefore, √2/3 is irrational.
4. **87.9821**: This is a finite decimal, which can be expressed as a fraction (879821/10000). Thus, it is a rational number.
The only irrational number from the provided choices is **√2/3**.
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