[\begin{array}{c}-4 \ -3.4\end{array}]－ $[-0.6]=$
Answer (2)
To evaluate the expression [ − 4 − 3.4 ] − [ − 0.6 ] , we first calculated it step-by-step. The results yielded [ − 4 − 3.4 ] = − 8 and [ − 0.6 ] = − 1 , leading to the final calculation of − 8 − ( − 1 ) = − 7 . Thus, the final result is − 7 .
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Calculate the value of the fraction: − 3.4 − 4 ≈ 1.17647 .
Find the greatest integer less than or equal to − 3.4 − 4 : [ − 3.4 − 4 ] = 1 .
Find the greatest integer less than or equal to − 0.6 : [ − 0.6 ] = − 1 .
Calculate the final result: 1 − ( − 1 ) = 2 .
Explanation
Understanding the Problem We are asked to evaluate the expression [ − 3.4 − 4 ] − [ − 0.6 ] , where [ x ] denotes the greatest integer less than or equal to x . This is also known as the floor function.
Calculating the Fraction First, we need to calculate the value of − 3.4 − 4 . Since both the numerator and denominator are negative, the result will be positive. We have − 3.4 − 4 = 3.4 4 = 34 40 = 17 20 ≈ 1.17647 .
Finding the First Floor Value Next, we need to find the greatest integer less than or equal to 17 20 . Since 17 20 ≈ 1.17647 , the greatest integer less than or equal to this value is 1. Therefore, [ − 3.4 − 4 ] = 1 .
Finding the Second Floor Value Now, we need to find the greatest integer less than or equal to − 0.6 . Since − 0.6 is between − 1 and 0 , the greatest integer less than or equal to − 0.6 is − 1 . Therefore, [ − 0.6 ] = − 1 .
Calculating the Final Result Finally, we need to calculate the difference: [ − 3.4 − 4 ] − [ − 0.6 ] = 1 − ( − 1 ) = 1 + 1 = 2 .
Final Answer Therefore, the value of the expression is 2.
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 of size 10 and you want to access the element at index x , where x is a real number, you would use the floor function to find the integer index. Another example is in calculating income taxes, where the tax brackets are defined by integer values, and the floor function can be used to determine which tax bracket a person falls into based on their income.
