Math Operators and Expressions in Java

Increment and Decrement Operators

• The ++ operator increments a variable by 1.
• The -- operator decrements a variable by 1.

Integer Division and Remainder

• Integer division (/) returns the whole number result of the division.

Powers and Roots

• The Math class provides methods for computing square roots (sqrt) and powers (pow).
• To compute xn, use Math.pow(x, n).
• For computing x2, it's more efficient to use x * x.

Analyzing an Expression

• An expression is a combination of variables, literals, operators, and method calls.
• Parentheses control the order of computation.
• Multiplication and division have higher precedence than addition and subtraction.
• Combining integers and floating-point values results in a floating-point value.

Mathematical Methods

• The Math class contains static methods for various mathematical operations.

Converting Floats to Ints - Rounding

• The Math.round() method converts a floating-point number to the nearest integer.

Converting Floats to Ints - Casting

• Casting converts a value to a different type.
• Use (int) to convert a floating-point value to an integer.
• Casting discards the fractional part.

Reading Input

• System.in has limited features and requires other classes to be useful.
• The Scanner class reads keyboard input.
• Import the Scanner class: import java.util.Scanner;
• Create a Scanner object: Scanner input = new Scanner(System.in);
• Use methods like nextInt(), nextDouble(), nextLine() to read input.

Formatted Output

• The printf method controls the formatting of output.
• Use %.2f to format a floating-point number with two decimal places.
• You can specify a field width using %10d for an integer, which will print 10 characters with padding.

Fundamental Data Types

• Every value in Java is either a reference to an object or one of the primitive types.
• Java has eight primitive types:
  • Four Integer types: byte, short, int, long
  • Two Floating-point types: float, double
  • Two others: char, boolean

Number Types

• byte: A single byte with a range of -128 to 127
• short: A short integer with a range of -32768 to 32767
• int: An integer with a range of -2,147,483,648 to 2,147,483,647
• long: A long integer with a range of -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807
• float: A single-precision floating-point type with a range of about ±1038 and about 7 significant decimal digits
• double: A double-precision floating-point type with a range of about ±10308 and about 15 significant decimal digits
• char: A character representing code units in the Unicode encoding scheme
• boolean: A type with two truth values: false and true

Overflow

• Overflow occurs when the result of a computation exceeds the range of the number type.
• Generally, use int for integers.
• If overflow occurs, the result is truncated to fit within the range of the number type, without warning.
• Use long to avoid overflow in cases where the int range isn't sufficient.
• Overflow is less common with the double data type.

Rounding Errors

• Rounding errors occur when an exact representation of a floating-point number is not possible.
• Floating-point numbers have limited precision.
• Use double in most cases.

Constants: static final

• Declare constants with the static final keyword when they are used in multiple methods.
• static indicates that the constant belongs to the class, not the objects.
• final ensures that the constant value cannot be changed.
• Format: public static final dataType CONSTANT_NAME = value;

Calling Static Methods

• Do not call methods directly on number types like 12.5.sqrt().
• Use static methods like Math.sqrt(12.5).
• Static methods are declared inside classes and do not operate on objects.

String Type

• A string is a sequence of characters.
• A string variable can be created using a string literal, enclosed in double quotes.

String Method - length()

• The length() method returns the number of characters in a string.

Concatenation

• The + operator concatenates strings.
• Concatenating a string and a number converts the number to a string.

String Method - toUpperCase()

• The toUpperCase() method converts all characters in a string to uppercase.

String Method - replace()

• Replaces all instances of a substring in a string with a new substring.

String Input - next() method

• Reads the next token from the input stream, up to the next whitespace character.

Escape Sequences - \" and \\

• \" is used to include a quotation mark as part of a string.
• \\ is used to include a backslash as part of a string.

Escape Sequences - \n

• \n inserts a newline character.

Strings and Characters

• A string is a sequence of Unicode characters.
• A character is a value of type char.
• Character literals are enclosed in single quotes.

Four Basic Arithmetic Operators

• Addition: +
• Subtraction: -
• Multiplication: *
• Division: /

Integer Division

• Returns the whole number result of the division.

Modulus Operator (%)

• Returns the remainder of an integer division.

This quiz covers various mathematical operators and expressions in Java, including increment and decrement operators, integer division, and methods for powers and roots from the Math class. Understand how expressions are evaluated and the significance of operator precedence. Test your knowledge on converting floats to integers as well.