Is 5 1/25 a rational or irrational number
The correct answer and explanation is:
Correct Answer:
5 1/25 is a rational number.
Explanation (300 words):
To determine whether 5 1/25 is a rational or irrational number, we must understand the definitions of each:
- A rational number is any number that can be written as a fraction (or ratio) of two integers, where the denominator is not zero. Rational numbers include integers, terminating decimals, repeating decimals, and fractions.
- An irrational number is a number that cannot be expressed as a simple fraction. It has a non-terminating, non-repeating decimal expansion (e.g., √2, π, or e).
Now let’s look at 5 1/25 more closely:
This is a mixed number, which combines a whole number (5) and a fraction (1/25). To check whether it’s rational, convert it to an improper fraction: 5125=(5×25)+125=125+125=126255\frac{1}{25} = \frac{(5 \times 25) + 1}{25} = \frac{125 + 1}{25} = \frac{126}{25}
Now, 12625\frac{126}{25} is clearly a fraction of two integers: 126 and 25. The denominator (25) is not zero, so this is a valid rational number.
We can also convert it into a decimal: 5125=5+125=5+0.04=5.045\frac{1}{25} = 5 + \frac{1}{25} = 5 + 0.04 = 5.04
The decimal 5.04 is a terminating decimal, which is a hallmark of rational numbers.
Conclusion:
Since 5 1/25 can be written as both a fraction 12625\frac{126}{25} and a terminating decimal 5.04, it meets all criteria of a rational number. It is not irrational because it can be precisely expressed as a ratio of integers.
So, 5 1/25 is a rational number. ✅