Java

1. Java Math Class

2. What is the Math Class? • The Math Class is another class that is prepared by Java for us to use • We use this class for mathematical operations • The Math Class contains many different complex mathematical functions

3. Do you remember? • When we used the external class Scanner we had to use; • To make use of the Math class, this is not needed. • It is automatically imported Import Java.util.*;

4. How to use the Math Class • You must include the class name Math each time you wish to use the Math Class • Example; System.out.println(Math.pow(2,8)); Indicating you wish to output something Calling the Math Class Calling the function power Arguments (will work out 28)

5. What happens… • In the code above the function power is being used • The arguments being used are 2 and 8 • The program should output 256 • Why? 28 = 256 System.out.println(Math.pow(2,8));

6. System.out.println(Math.pow(2,8)); Problem? • By using the code above the result of 256 is not being saved anywhere as it is just simply an output • To save the result we need to use the following code double result = Math.pow(2,8); System.out.println(result);

7. Fed up of writing Math … • Programmers are lazy and do not enjoy writing the same things a number of times • We could use a java statement to avoid this, this is known as a static import statement (always placed before we create a class) import static.java.lang.Math.*;

8. … • Once we use the static import statement the code to use the power function would be much shorter. • The Math keyword no longer needs to be used double result = pow(2,8);

9. Math Class Functions Math.pow() – To the power of Math.sqrt() – The square root Math.abs() – Outputs only positive numbers Math.random() – Outputs a random number Math.round() – Rounds up numbers Math.ceil() – Outputs the smallest number Math.floor() – Outputs the largest number

10. Math.pow() • The Math.pow() works out the power of a certain number. • For example if we wish to find the answer of 29 we would use the following code

11. import static java.lang.Math.*; class Power { public static void main (String args[]){ int a = 2; int b = 9; double p = pow(a,b); System.out.println(p); } }

12. Math.sqrt() • The Math.sqrt() function is used when we want to find the square root of a number • For example we want to find the square root of 100 and 10000

13. import static java.lang.Math.*; class SquareRoot { public static void main (String args[]){ int a = 100; int b = 10000; double sr1 = sqrt(a); double sr2 = sqrt(b); System.out.println("The square root of 100 is " + sr1 + "\nThe square root of 10000 is " + sr2); } }

14. Math.abs() • The Math.abs() function gives the absolute value of the number • The absolute value of a number is equal to the same number without the sign. • It is useful on calculations which require positive numbers only • We would use Math.abs() to find the square root of a negative number (which cannot be done), so first we find out the absolute value.

15. import static java.lang.Math.*; class SquareRoot { public static void main (String args[]){ double a = -20.2; double positive = abs(a); System.out.println(positive); } }

16. Activity Using the Math functions we have leant so far • Create a program that will find; • 75 • Square root -90

17. Math.random() • This functions outputs a random number from a given group of numbers • This could be used in many games as a dice • The random function works with double data type only hence we would need to typecast this into a int not to get decimal numbers.

18. … • The random function also outputs 0 as a random number, if you wouldn’t like this to happen you must use the +1 function • For example you want to represent a dice so you only want numbers from 1 to 6 intdice = (int)(Math.random()*6)+1;

19. import static java.lang.Math.*; class RandomDice{ public static void main(String args[]){ int dice = (int)(random()*6)+1; System.out.println("Player one roll "+ dice); } }

20. Activity Using the Math functions we have leant so far • Coin Toss Assume that; • Heads = 1 • Tails = 2 Write a program that generates a random number between 1 and 2 to represent heads and tails

21. Math.round() • The Math.round() function results in the closest value to the integer • If the fraction value is 1.7, it will add 1 to 7 and output 8 • Basically the Math.round() function would output the whole number with no decimal

22. import static java.lang.Math.*; class round{ public static void main(String args[]){ double num1 = round(1223.444); double num2 = round(34.88); System.out.println(num1 + "\n" + num2); } }

23. Math.ceil() • The Math.ceil() also outputs decimal numbers as whole numbers • This is done in a different way as it will return the smallest whole number which is not less than the number given • For example; • 13.3 would result in 14 • -11.5 would result in -11

24. import static java.lang.Math.*; class ceil{ public static void main(String args[]){ double num1 = ceil(10.1); double num2 = ceil(-43.4); System.out.println(num1 + "\n" + num2); } }

25. Math.floor() • The Math.floor() does the exact opposite to Math.ceil() • The whole number would be the next largest number possible • For example; • 13.3 would result in 13 • -11.5 would result in -12

26. import static java.lang.Math.*; class floor{ public static void main(String args[]){ double num1 = floor(10.1); double num2 = floor(-43.4); System.out.println(num1 + "\n" + num2); } }

27. Formatting values Number of decimal places to be printed

28. Output of Results • So far we should know how to use; • print() • println() • Now we will be using printf() which is used to determine how many decimal places we would like our result to have

29. Placeholders • The following are the placeholders we will be using %f only

30. Decimal Places • When using %f the number of decimal places can be specified • What happens? • %.2f = determines that you want 2 decimal places (replaces the actual answer) • \n is used to display the actual answer on the “next line” double num1 = 234.8889; double num2 = 56.99058; double ans = num1+num2; System.out.printf(“Formatted to 2 decimal places :%.2f\n”,ans);

31. import static java.lang.Math.*; class PrintFDemo { public static void main (String args[]) { double num1 = 234.8889; double num2 = 56.99058; double ans = num1+num2; System.out.printf("Formatted to 2 decimal places :%.2f\n",ans); } }

32. Field Size • A field can also be used to hold a specific number. This means how many characters are to be held • For example we want to have a field size of 8 this mean only 20 numbers can be held double num1 = 234.8889; double num2 = 56.99058; double ans = num1+num2; System.out.printf(“Formatted to field size 20:%20.3f\n”,ans);

33. import static java.lang.Math.*; class feild { public static void main (String args[]) { double num1 = 234.8889; double num2 = 56.99058; double ans = num1+num2; System.out.printf("Formatted to 3 decimal places and a field size of 20 :%20.3f\n",ans); } }

34. Padding with 0s • From the output above we would see that there are many empty spaces before the number in order to use the 20 field spaces • We might wish to pad (fill) these spaces with 0s all you have to do is add a 0 in front of your placeholder double num1 = 234.8889; double num2 = 56.99058; double ans = num1+num2; System.out.printf(“Formatted to field size 20:%020.3f\n”,ans);

35. import static java.lang.Math.*; class feild { public static void main (String args[]) { double num1 = 234.8889; double num2 = 56.99058; double ans = num1+num2; System.out.printf("Formatted to 3 decimal places and a field size of 20 :%020.3f\n",ans); } }