Identify the two rational numbers.
A. $-\frac{2}{5}$
B. $1.010010001 \ldots$
C. $\sqrt{7}$
D. 1.01
Answer (1)
A rational number can be expressed as a fraction q p , where p and q are integers and q = 0 .
− 5 2 is a rational number because it is a fraction of two integers.
1.01 is a rational number because it can be written as 100 101 .
The two rational numbers are A , D .
Explanation
Problem Analysis We are given four numbers and we need to identify which two are rational. A rational number is a number that can be expressed as a fraction q p , where p and q are integers and q = 0 . Let's analyze each option.
Analyzing Option A A. − 5 2 is a fraction where both the numerator (-2) and the denominator (5) are integers. Therefore, it is a rational number.
Analyzing Option B B. 1.010010001 … is a non-repeating, non-terminating decimal. This means it cannot be expressed as a fraction of two integers, so it is an irrational number.
Analyzing Option C C. 7 is the square root of a non-perfect square. The square root of a non-perfect square is an irrational number. Therefore, 7 is irrational.
Analyzing Option D D. 1.01 is a terminating decimal. It can be written as 100 101 , where 101 and 100 are integers. Therefore, it is a rational number.
Final Answer The two rational numbers are A and D.
Examples
Rational numbers are essential in everyday calculations, from dividing a pizza equally among friends to understanding financial ratios. For instance, if you have a recipe that calls for 3 2 cup of flour and you want to make half the recipe, you need to calculate 2 1 × 3 2 = 3 1 cup of flour. Understanding rational numbers allows you to accurately adjust quantities and proportions in various real-life situations, ensuring precise and consistent results.
