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Math With Java

Math With Java. The Math Class. First, A Quick Review of Math Operators in Java. Primitive Data type in Java that represent numbers: int – Integer numbers double – Numbers with a decimal Ex. double myValue = 10.5;//store 10.5 in the variable

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Math With Java

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  1. Math With Java The Math Class

  2. First, A Quick Review of Math Operators in Java • Primitive Data type in Java that represent numbers: • int – Integer numbers • double – Numbers with a decimal • Ex. • double myValue = 10.5;//store 10.5 in the variable • intmyInt = 7;//stores 7 in the variable myInt • The math operators for int and double are: • * multiplication • / division • + addition • - subtraction • % remainder (only for int)

  3. Casting • When data types are converted, we use a technique called casting to tell java to do the conversion for us • When conversion results in a loss of data, the casting must be told to java • Ex. double dVal = 10.5; int iVal = dVal;//error, you will lose 0.5 • To tell java that you are OK with losing the 0.5 you have to rewrite the line as: int iVal = (int)dVal;//(int) tells java you are aware of the possible loss of data • Ex. int iVal = 7; double dVal = iVal; • No problem this time, no information would be lost when storing an int in a double.

  4. What is printed int iVal1 = 6; int iVal2 = 10; double dVal1 = 4.0; double dVal2 = 3.0; • System.out.println( iVal2 / (int)dVal1); // 2 • System.out.println( iVal2 / (double)iVal1); //1.6666667 • System.out.println( (double)iVal2 / (int)dVal1); //2.5 • System.out.println( (int)dVal2 / (int)dVal1); //1 • System.out.println( (int)dVal1 / iVal1); //0

  5. Integer Remainder • So what happens to the decimal when dividing integers? • It is possible to find out how much was left over in the division, also known as the remainder • For example, • 5 / 3 is 1 remainder 2 • 7 / 2 is 3 remainder 1

  6. (%) Mod Operator • With integers, the % operator determines the remainder after division has occurred • Ex. • 10 % 6 = 4 • 12 % 4 = 0 • 32 % 5 = 2 • 18 % 5 = 3

  7. Mod Operator • Mod Operator has many uses, one common one is telling time • If 350 minutes have past since midnight, what time is it? • There are 60 minutes in an hour • 350 / 60 = 5 • 350 % 60 = 50 • The time is 5:50am

  8. New - Shortcut Operators • Some operators are shortcuts to common expressions:

  9. The Math Class • The Math class is a special class called a static class, there is no need to create a Math object, instead we ask the class directly • Static class • Math.PI//value of PI • Non static class • String PI = “3.14”;//make a new string

  10. Math class • All of the buttons you find on your calculator are in the Math class • sin, cos, tan • sqrt, pow, etc. • Of course you can find them all in the JavaDoc • Another things you’ll need to use in the Math class is random numbers

  11. Numeric Operations • The Math class can be used by putting the following line under the package statement: • import java.lang.Math; • import – command tells java to get code from another library

  12. Math Methods • double Math.ceil( double value ) • This method rounds up a floating point number • It also returns a floating point so be sure to cast if you’re putting the result in an int • Ex. • double ceil = Math.ceil( 10.9 ); //returns 11.0 • double ceil = Math.ceil( 3.1 ); //returns 4.0 • double ceil = Math.ceil( -1.9 ); //returns -1.0 • int ceil = (int)Math.ceil( -1.2 ); //returns -1.0

  13. Math Methods • double Math.floor( double value ) • This method rounds down a floating point number • It also returns a floating point so be sure to cast if you’re putting the result in an int • Ex. • double floor = Math.floor( 3.1 ); //returns 3.0 • double floor = Math.floor( 10.9 ); //returns 10.0 • double floor = Math.floor( -1.2 ); //returns -2.0 • int floor = (int)Math.floor( -1.9 ); //returns -2.0

  14. Math Methods • double Math.pow( double base, double exponent ) • This method returns the power of (base)exponent • It also returns a floating point so be sure to cast if you’re putting the result in an int • Ex. • double power = Math.pow( 2, 3 ); //returns 8.0 • double power = Math.pow( 3, 4 ); //returns 81.0 • double power = Math.pow( 0.1, 5 ); //returns 0.00001 • int power = (int)Math.pow( 1.5, 2 );//returns 2.25 (it is cast to 2)

  15. Math Methods • double Math.abs( double value ) • This method returns the absolute value of value • It also returns a floating point so be sure to cast if you’re putting the result in an int • Ex. • double absolute = Math.abs( 100 ); //returns 100.0 • double absolute = Math.abs( -4.5); //returns 4.5 • double absolute = Math.abs( 0.57 ); //returns 0.57 • int absolute = (int)Math.abs( -1234 ); //returns 1234

  16. Math Methods • double Math.sqrt( double value ) • This method returns the square root of value • It also returns a floating point so be sure to cast if you’re putting the result in an int • Ex. • double root = Math.sqrt( 100 ); //returns 10.0 • double root = Math.sqrt( 2 ); //returns 1.4142 • double root = Math.sqrt( 0.25 ); //returns 0.5 • int root = (int)Math.sqrt( 16.0 ); //returns 4

  17. Making a Formula in Java • The quadratic formula: • Using the order of operations we get, x1 = ( –1*b + Math.sqrt( Math.pow( b, 2 ) – 4*a*c ) ) / 2*a Can you rewrite the other solution? x2 = (–1*b – Math.sqrt( Math.pow( b, 2 ) – 4*a*c )) / 2*a

  18. Math.random() • Random numbers can be generated from the random method of the Math Class • static double random(); • returns a random number between 0.0 (inclusive) and 1.0 (exclusive) • Ex. • double randomNumber = Math.random() * 100; • This is a random number between 0.0 and 99.999999

  19. Using Math.random • Ex. • double randomNumber = Math.random() * 35; • Between 0.0 and 34.9999999999 • double randomNumber = Math.random() * 50 + 10; • Between 10.0 and 59.999999999 • int randomNumber = (int)(Math.random() * 20) + 5; • Between 5 and 24 • don’t forget to cast with ints • Notice the range is 5 to 24! • Math.random() * 20 returns 0 to 19.999999999999… • (int)(Math.random() * 20) chops off all decimals • Returns 0 to 19

  20. Be Careful When Casting! • (int)Math.random() * 20 + 5; • returns 5 every time your program is run: • Generate a random value, say 0.774312 • Cast it to an it • Now it has the value 0 • 0 * 20 = 0 • 0 + 5 = 5

  21. Using Math.random • If you want to generate a number in the range [a,b)  not including b (as doubles) • Math.random()*(b – a) + a • If you want to generate a number in the range [a,b] (as ints) • (int)(Math.random()*(b – a+1)) + a

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