One rational number between -3 and -2 is:
i) 3
ii) [tex]$-5 / 2$[/tex]
iii) [tex]$-7 / 2$[/tex]
iv) none of these
Answer (2)
The rational number between -3 and -2 is − 2 5 , as it falls within the specified range. The other options do not meet the criteria. Therefore, the correct option is − 2 5 .
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Convert the given options to decimal form: − 5/2 = − 2.5 and − 7/2 = − 3.5 .
Check if each option lies between -3 and -2.
Determine that − 3 < − 2.5 < − 2 is true.
Conclude that the rational number between -3 and -2 is − 2 5 .
Explanation
Problem Analysis and Conversion to Decimals We need to find a rational number that lies between -3 and -2. The given options are 3, -5/2, -7/2, and none of these. To easily compare these numbers, let's convert the fractions to decimals.
Listing the Options and Condition The options are: i) 3 ii) − 5/2 = − 2.5 iii) − 7/2 = − 3.5 Now, we need to check which of these numbers falls between -3 and -2. In other words, we are looking for a number x such that − 3 < x < − 2 .
Checking Each Option Let's examine each option: i) 3: Is − 3 < 3 < − 2 ? No, 3 is not less than -2. ii) − 5/2 = − 2.5 : Is − 3 < − 2.5 < − 2 ? Yes, -2.5 is between -3 and -2. iii) − 7/2 = − 3.5 : Is − 3 < − 3.5 < − 2 ? No, -3.5 is less than -3.
Identifying the Correct Option Since − 3 < − 2.5 < − 2 , the rational number − 5/2 lies between -3 and -2.
Final Answer Therefore, the correct answer is − 5/2 .
Examples
Understanding rational numbers and their placement on the number line is crucial in various real-life scenarios. For instance, when dealing with financial transactions, stock prices, or temperature measurements, we often encounter values that fall between two integers. Knowing how to identify and work with these rational numbers allows for more precise calculations and decision-making. For example, if you need to determine if a stock price of "-2.5" dollars falls within a certain investment range of "-3" to "-2" dollars, you would use the same principles as in this problem to confirm its position on the number line.
