Arithmetic Notes and Program Assignments
Operators
Binary Operators:
Operation
Addition
Subtraction
Multiplication
Division
Computer
+
*
/
or
% - modulus
When using the forward slash (/) for dividing two integers, the result will just give the integer quotient
for the result.
Example: 8 / 2 is 4 but 7 / 2 is 3 (the decimal part of the answer is not given)
When dividing two double numbers, the result is a double number so 7.0 / 2.0 is 3.5
Modulus (%) - is used to get the remainder when doing division with integers.
Example: 8 % 2 is 0 since 2 goes into 8 evenly, the remainder is 0.
7 % 2 is 1 since 2 does not go into 7 evenly, the remainder is 1.
Order of Operation - follows the same rules as Algebra
Parenthesis
Multiplication and Division – from left to right
Addition and Subtraction - from left to right
Unary Arithmetic Operators:
1)
+ or -  simply makes the number positive or negative (+ rarely used since the number
is automatically positive)
2) increment and decrement operators: ++ and - adds or subtracts 1 from the variable
Examples:
a) num = 10;
num = num + 1; is the same as num++;
b) num = 10;
num = num – 1;
is the same as num--;
or ++num;
or --num;
c) x = 10;
y = ++x; //x now has a value of 11 and so does y
d) x = 10;
y = x++; //x now has a value of 11 and y has a value of 10
// assignment to y done first then 1 added to x
e) x = 10;
x = x++; // x has a value of 10 at the end of execution!
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Arithmetic Notes and Program Assignments
// the right hand side ++ value of 11 is never stored in x
Combined Assignment Operators:
+=, -=, *=, /=
Examples:
a) y -= 3  same as y = y – 3
b) y /= 3  same as y = y / 3
c) y += 3  same as y = y + 3
Math Methods
No symbol for powers or roots
*Use Math.sqrt method - to find the square root
double squareRoot = Math.sqrt(x);
*Use Math.pow method to raise a number to a power
double power = Math.pow(x, n); //x is the base and n is the exponent
Other Math methods:
Math.sin(x)
Math.asin(x)
Math.cos(x)
Math.acos(x)
Math.tan(x)
Math.atan(x)
Math.round(x) – closest integer
Math.ceil(x) – smallest integer
Math.toRadians(x)
*Math.abs(x)
Math.max(x, y) - the larger of x or y
Math.min(x, y) – the smaller of x or y
Math.exp(x) - ex
Math.log(x) – natural log
Math.log10(x) – Decimal log
Math.floor(x) – largest integer
Math.toDegrees(x)
*Math.random() – returns a double in the range of [0.0, 1.0)
* May be included on the AP exam
Formatting numbers:
Format String
“%d”
“%5d”
“Quantity: %5d”
“%f”
“%.2f”
“%7.2f”
“%s”
%d %.2f
Example:
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Format Specifier Examples
Sample Output
Comments
24
Use d with an integer
24
Spaces are added so that the field width is 5
Quantity: 24
Characters inside a format string but outside a
format specifier appear in the output
1.21997
Use f with a floating-point number
1.22
Prints two digits after the decimal point
1.22
Spaces are added so that the field width is 7
Hello
Use s with a string
24 1.22
You can format multiple values at once
System.out.printf(“Quantity: %d Total: %10.2f”, quantity, total);