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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.
Answer for screen readers

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

Steps to Solve

  1. 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:

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

  1. 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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