[2024] [x] x [1.99]=1 [-1.02]=-2 [-3.4] [-0.6]=
Answer (2)
The final result of evaluating the expression using the floor function is − 3 . This is determined by first evaluating the individual floor values of [ − 3.4 ] and [ − 0.6 ] , which are − 4 and − 1 respectively, and then performing the subtraction. Therefore, the overall result of the expression is − 3 .
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Evaluate [ − 3.4 ] as − 4 .
Evaluate [ − 0.6 ] as − 1 .
Calculate the difference: − 4 − ( − 1 ) = − 4 + 1 .
The final result is − 3 .
Explanation
Understanding the Problem We are asked to evaluate the expression [ − 3.4 ] − [ − 0.6 ] , where [ x ] denotes the greatest integer less than or equal to x . This is also known as the floor function.
Evaluating [-3.4] First, we need to find the value of [ − 3.4 ] . The greatest integer less than or equal to − 3.4 is − 4 . Think of a number line; − 3.4 lies between − 4 and − 3 . Since we want the greatest integer that is less than or equal to − 3.4 , we choose − 4 .
Evaluating [-0.6] Next, we need to find the value of [ − 0.6 ] . The greatest integer less than or equal to − 0.6 is − 1 . On the number line, − 0.6 lies between − 1 and 0 . The greatest integer less than or equal to − 0.6 is − 1 .
Final Calculation Now, we subtract the two values: [ − 3.4 ] − [ − 0.6 ] = − 4 − ( − 1 ) = − 4 + 1 = − 3 .
Final Answer Therefore, the final answer is − 3 .
Examples
The floor function is used in computer science to determine the index of an array or a list. For example, if you have an array and you want to access an element using a floating-point number, you can use the floor function to convert the floating-point number to an integer index. Also, in everyday life, if a store offers a discount like 'everything under $50.00 is 10% off', the floor function helps determine which items qualify. If an item costs 49.99 , [49.99] = 49$, confirming it's under $50 and eligible for the discount.
