Is 5 1/25 rational or irrational?

Understand the Problem

The question is asking whether the number 5 1/25, which is a mixed number, is classified as a rational or irrational number. To address this, we need to convert it into an improper fraction or decimal and analyze its properties.

Answer

The number $ 5 \frac{1}{25} $ is a rational number.

Steps to Solve

Convert the mixed number to an improper fraction

To convert the mixed number ( 5 \frac{1}{25} ) to an improper fraction, use the formula:

$$ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} $$

For our case:

$$ 5 \frac{1}{25} = \left(5 \times 25 + 1\right) / 25 = \left(125 + 1\right) / 25 = \frac{126}{25} $$

Determine if the fraction is rational or irrational

A number is considered rational if it can be expressed as a fraction of two integers (where the denominator is not zero). The fraction ( \frac{126}{25} ) consists of two integers (126 and 25), and since the denominator (25) is not zero, it is a rational number.

The number ( 5 \frac{1}{25} ) is a rational number.

More Information

Rational numbers can always be expressed as fractions or terminating/repeating decimals. In this case, ( \frac{126}{25} ) can be divided to obtain a decimal form, approximately ( 5.04 ), which confirms it is a rational number.

Tips

Confusing mixed numbers with decimals. Always remember that mixed numbers can be converted into improper fractions to determine their classification.
Assuming that all numbers with decimals are irrational; many decimals can be rational.

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