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Using Numbers

Using Numbers. Chapter 3. Data Types. Traditionally, programming languages have assigned different types of data for different types of numbers. In many languages, there may be several numeric data types, perhaps six.

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Using Numbers

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  1. Using Numbers Chapter 3

  2. Data Types • Traditionally, programming languages have assigned different types of data for different types of numbers. • In many languages, there may be several numeric data types, perhaps six. • These different numeric data types developed because different amounts of memory were needed to store different kinds of numbers. • Fortunately, Python has just two data types: int (for integers) and float (for decimal numbers)

  3. 2 data types • Integers are just whole numbers, and can be positive or negative • Floats are numbers including fractions, expressed with a floating point (decimal). • When we type a “literal” (when we hard code a value into our program), Python recognizes whether that number is an integer or a float number, and assigns the correct data type.

  4. Example of numeric data types • # change.py • # A program to calculate the value of some change in dollars • def main(): • print "Change Counter" • print • print "Please enter the count of each coin type." • quarters = input("Quarters: ") • dimes = input("Dimes: ") • nickels = input("Nickels: ") • pennies = input("Pennies: ") • total = quarters * 0.25 + dimes * 0.10 + nickels * .05 + pennies * .01 • print • print "The total value of your change is", total • main()

  5. Workshop • Alter the change.py program so that you also count half-dollars and dollars (Kennedy and Susan B. Anthony coins)

  6. The type() function • Python has a built-in function, type(), which tells us which data type a variable is. Just put the variable name between the parentheses. • Example: if you type newVar = 58 into the Python interpreter, then type(newVar), the result displayed will be <type ‘int’>

  7. Workshop • In the Python interpreter, use the type() function to test the following variables: • num_units = 10 • num_students=25 • subtotal = 95.60 • score1 = 87 • average = 81.5 • users_online = 112 • total = 234.73

  8. Operators and Operations • Python performs the basic math operations on both numeric data types

  9. What is exponentiation? • Exponentiation refers to the power, or exponent, of a number. For example, 24 refers to two to the power of four, or 2*2*2*2. • In Python, you can use the exponentiation operator, **, to find the value of exponentiation. • 24 = 2 ** 4 = 16 • Try it in the Python interpreter

  10. What is remainder? • You all know what the remainder is… the value that is left after division, if there is any value (other than zero) left at all. • E.g., the remainder of 10/7 is 3. • In Python, we would express this as 10 % 7 • Workshop: Use the interpreter to find the remainders:200/23, 17/4, 25/3, 28/9, 100/12, 10/6

  11. What is absolute value? • The absolute value of a number is its numerical value regardless of its sign, that is, whether it’s negative or positive. • The built-in Python function abs() will always return a number’s absolute value. • The absolute value of 107 is 107; the absolute value of -33 is 33. • Workshop: use the interpreter to verify these absolute values

  12. The Math library • There is a suite of built-in functions in Python that handle mathematical functions. See Table 3.2 in our textbook, p. 57 • To have access to all these built-in functions in Python, we need first to invoke the library: import math, the very first line of the program

  13. Special Math Library functions • We’ll limit our use of the Math library to one “property” (built-in data) and three functions. • Pi is an approximate value for pi, or 3.14159….. In Python, this gets expressed as math.pi • exp(x) will give the exponential of x • ceil(x) gives the smallest whole number greater than or equal to x • and floor(x) gives the largest whole number less than or equal to x

  14. Workshop • In teams of two, write a program which asks the user for the radius of a circle and then calculates the area of that circle.

  15. Workshop • In teams of two, write a program that asks the user for a float number and then rounds that number up and down.

  16. Integer limits and the L data type • Sometimes integer calculations produce an integer so huge it exceeds a language and computer’s ability to display it. In other words, the number exceeds memory allocations. • When a number exceeds memory, we get an Overflow error • Very long/short floats in Python will be represented in scientific, or exponential, notation. e+n will be added to the end of the number, indicating that 10n should be added to the number, where n is a power of 10.

  17. Long ints • There is a third data type, long ints, which handle huge numbers. The memory allocated for a long int, or L, is flexible, not fixed like floats or integers. • When declaring a literal number, you can create a long int by just adding L to the end.21349L • New versions of Python automatically convert humongous integers to long ints. • Except when huge numbers are expected, you should always use the int type, because it’s much faster to compute.

  18. Type conversion • Often it is necessary to convert one data type to another, since arithmetic operations on a computer are different for integers and floats. • Automatic type conversion: When there is a mixed-type expression, Python will automatically convert an integer to a float to perform the operation:average_wgt = 507.5/7 • Seven will automatically be converted to a float, and average_wgt will be a float.

  19. Explicit type conversion • Sometimes we have to force a type conversion. For example, if we’re trying to find an average, and both factors are integers, the result may well be a float. But unless we tell Python to produce a float, it will whack off the fraction and return an integer. • num_students = 12 • sum = 1005 • avg = sum/num_students • This will produce an integer; we need a float

  20. The solution is to force the result into the float type:avg = float(sum/num_students) • Python provides similar type conversion functions for integers and long integers: • >>>myInt = int(3.3)>>>print myInt3 • >>>myLInt = long(6.7)>>>print myLInt6L

  21. Rounding • Python also has a built-in function, round(), which rounds a float to the nearest whole float value • >>>round(7.1490)7.0 • We can then convert the rounded number into an integer, if we wanted:>>>int(round(7.1490))7

  22. Workshop: in pairs • Write a program which gets a number between 1 and 10 from the user and which also gets a random number from the computer. Print both so the user can compare the values. • The first line of your program should be import random • To generate a random number, type random.random()

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