Convert the decimal 0.83 to a fraction, and classify it as either rational or irrational.
A) $83 / 10$, irrational
B) $83 / 100$, rational
C) $83 / 10$, rational
D) $83 / 100$, irrational
Answer (2)
The decimal 0.83 can be converted to the fraction 100 83 , which is classified as a rational number. Thus, the correct answer is B) 100 83 , rational.
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Convert the decimal 0.83 to a fraction by recognizing the place value: 100 83 .
Determine if the fraction is rational or irrational.
Since 83 and 100 are integers, 100 83 is a rational number.
The answer is 100 83 , rational.
Explanation
Problem Analysis We are given the decimal 0.83 and asked to convert it to a fraction and classify it as either rational or irrational.
Converting Decimal to Fraction To convert the decimal 0.83 to a fraction, we observe that there are two digits after the decimal point. This means we can write it as a fraction with a denominator of 100. Thus, 0.83 can be written as 100 83 .
Rational vs Irrational Numbers Now we need to classify the fraction 100 83 as either rational or irrational. A rational number is a number that can be expressed in the form q p , where p and q are integers and q = 0 . An irrational number cannot be expressed in this form.
Classification Since 83 and 100 are both integers, the fraction 100 83 is a rational number.
Final Answer Therefore, the decimal 0.83 can be expressed as the fraction 100 83 , and it is a rational number.
Examples
Understanding rational numbers is crucial in everyday situations, such as calculating proportions or percentages. For instance, if you score 83 out of 100 on a test, that's 83%, which can be represented as the rational number 100 83 . This concept is also used in cooking when adjusting recipes, or in finance when calculating interest rates or discounts. Rational numbers provide a precise way to express and work with parts of a whole.
