Java Programing: Predefined mathematical methods that are part of the class Math

Question

Java Programing:

Predefined mathematical methods that are part of the class Math in the package java.lang include those below.

method name

description

abs( m )

returns the absolute value of m

ceil( m )

rounds m to the smallest integer not less than m

floor( m )

rounds m to the largest integer not greater than m

max( m , n )

returns the larger of m and n

min( m , n )

returns the smaller of m and n

pow( m , n )

returns m raised to the power n

round( m )

returns a value which is the integer closest to m

sqrt( m )

returns a value which is the square root of m

Evaluate each of the following, which include Math predefined methods.

(1)       _____ Math.abs( 6.0 )              (2)       _____ Math.abs( - 6.0 )

(3)       _____ Math.ceil( 10.25 )           (4)       _____ Math.ceil( - 6.8 )

(5)       _____ Math.floor( - 5.1 )           (6)       _____ Math.floor( 7.9 )

(7)       _____ Math.pow( 5 , 2 )             (8)       _____ Math.pow( 2 , 5 )

(9)       _____ Math.max( 1.5 , 2 )           (10)     _____ Math. min( 3 , 0.5 )

(11)     _____ Math.min( 2 , 1.5 )           (12)     _____ Math. max( 0.5 , 3 )

(13)     _____ Math.sqrt( 16.0 )            (14)     _____ Math. round( 0.6 )

(15)     _____ Math.ceil( Math.pow( 3 , 0.5 ) )

(16)     _____ Math.floor( Math.pow( 1.5 , 2 ) )   

(17)     _____ Math.ceil( Math.floor( 3.5 ) )

(18)     _____ Math.min( Math.max( 3.0 , 2 ), 2.5)

(19)     _____ Math.max( Math.min( 2.0 , 3 ), 3.0)

(20)     _____ Math.sqrt( Math.pow( 2.0 , 3 ) )    

(21)     _____ Math.pow( Math.sqrt( 9 ) , 2 ) )

(22)     _____ Math.round( Math.max( 2.1 , 3.1 ) )

(23)     _____ Math.abs( Math.abs( 8.0 ) )

(24)     _____ Math.min( Math.abs( 1.5 , 2 ) )

(25)     _____ Math.ceil( Math.pow( 1 , 0.5 ) )

method name

description

abs( m )

returns the absolute value of m

ceil( m )

rounds m to the smallest integer not less than m

floor( m )

rounds m to the largest integer not greater than m

max( m , n )

returns the larger of m and n

min( m , n )

returns the smaller of m and n

pow( m , n )

returns m raised to the power n

round( m )

returns a value which is the integer closest to m

sqrt( m )

returns a value which is the square root of m

Explanation / Answer

import java.io.*;

public class math{
public static void main(String args[])
{

System.out.println("Solving some problem using inbuilt funstion of the math library:");
//Math.abs function can return the absolute value of int,double,float & long
System.out.println("Math.abs(6.0) :");
System.out.println(Math.abs(6.0));
System.out.println("Math.abs(- 6.0) :");
System.out.println(Math.abs(- 6.0));
System.out.println("Math.ceil(10.25) :");
//Math.ceil function returns the smallest double value that is greater than or equal to the argument and is equal to a mathematical integer.
System.out.println(Math.ceil(10.25));
System.out.println("Math.ceil(- 6.8) :");
System.out.println(Math.ceil(-6.8));
System.out.println("Math.floor(- 5.1) :");
//Math.floor function returns the largest double value that is less than or equal to the argument and is equal to a mathematical integer
System.out.println(Math.floor(-5.1));
System.out.println("Math.floor(7.9) :");
System.out.println(Math.floor(7.9));
//Math.pow returns the value of the first value raised to the power of the second
System.out.println("Math.pow(5,2) :");
System.out.println(Math.pow(5,2));
System.out.println("Math.pow(2,5) :");
System.out.println(Math.pow(2,5));
//Math.max function returns the maximum of the two values (it can be int/float/long/double)
System.out.println("Math.max(1.5,2) :");
System.out.println(Math.max(1.5,2));
//Math.max function returns the maximum of the two values (it can be int/float/long/double)
System.out.println("Math.min(3,0.5) :");
System.out.println(Math.min(3,0.5));
System.out.println("Math.min(2, 1.5) :");
System.out.println(Math.min(2,1.5));
System.out.println("Math.max(0.5,3) :");
System.out.println(Math.max(0.5,3));
//Math.sqrt function returns the correctly rounded positive square root of a double value.
System.out.println("Math.sqrt(16.0) :");
System.out.println(Math.sqrt(16.0));
//Math.round method returns the closest long to the argument.
System.out.println("Math.round(0.6) :");
System.out.println(Math.round(0.6));
System.out.println(Math.pow( 2.0 , 3 ));

System.out.println("Math.ceil(Math.pow( 3 , 0.5 )) :" );
System.out.println(Math.ceil( Math.pow( 3 , 0.5 ) ));
/*Math.pow will evaluate to 1.7320508075688772 as it will calculate 3 raised to the power 0.5
* then this value is passed to ceil function which rounds up the value to 2.0
*/
System.out.println("Math.floor(Math.pow(1.5 ,2)) :");
System.out.println(Math.floor( Math.pow( 1.5 , 2 ) ));
/*Math.pow will evaluate to 2.25 as it will calculate 1.5 raised to the power 2
* then this value is passed to ceil function which rounds up the value to 2.0
*/
System.out.println("Math.ceil(Math.floor(3.5)) : ");
System.out.println(Math.ceil(Math.floor(3.5)));
/*Math.floor will evaluate to 3.0 as it will round down the value 3.5
* then this value is passed to ceil function which makes no change because the value rounded
* up value of 3.0 is also 3.0 had it been 3.1 it would have made it 4.0
*/
System.out.println("Math.min(Math.max(3.0,2), 2.5) :");
System.out.println( Math.min( Math.max( 3.0 , 2 ), 2.5) );
/*Math.max will evaluate to 3.0 as it will compare the values 3.0 and 2 and return the larger one
* then this value is passed to min function which calculates the minimum value amongst 3.0 and 2.5
* and hence the entire expression evaluates to 2.5
*/
System.out.println("Math.max(Math.min(2.0,3),3.0) : ");
System.out.println( Math.max( Math.min( 2.0 , 3 ), 3.0));
/*Math.min will evaluate to 2.0 as it will compare the values 2.0 and 3 and return the smaller one which is 2.0
* then this value is passed to max function which compares the two values 2.0 and 3.0 and returns
* the maximum value amongst 2.0 and 3.0
* and hence the entire expression evaluates to 3.0
*/
System.out.println("Math.sqrt(Math.pow(2.0,3))");
System.out.println( Math.sqrt( Math.pow( 2.0 , 3 ) ));
/*Math.pow will evaluate to 8.0 as it will calculate 2.0 raised to the power 3
* then this value is passed to sqrt function which caculates the square root of 8.0
* and hence the entire expression evaluates to 2.8284271247461903
*/
System.out.println( "Math.pow(Math.sqrt( 9 ),2)");
System.out.println( Math.pow( Math.sqrt( 9 ) , 2 ) );
/*Math.sqrt will evaluate to 3.0 as it will calculate the square root of 9 which comes out to be 3.0
* then this value is passed to pow function which caculates the 3.0 raised to the power 2
* and hence the entire expression evaluates to 9.0
*/
//Similar expressions....
System.out.println("Math.round(Math.max(2.1,3.1))");
System.out.println(Math.round(Math.max( 2.1 , 3.1 ) ));
System.out.println("Math.abs(Math.abs(8.0)) :");
System.out.println(Math.abs(Math.abs( 8.0 )));
System.out.println("Math.min(Math.abs(1.5),2) : ");
System.out.println(Math.min(Math.abs( 1.5 ), 2 ) );
System.out.println("Math.ceil( Math.pow(1 ,0.5 )) :" );
System.out.println( Math.ceil( Math.pow( 1 , 0.5 ) ) );

}
}

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