268 lines
5.5 KiB
Markdown
268 lines
5.5 KiB
Markdown
[Contents](../Contents.md) \| [Previous (1.2 A First Program)](02_Hello_world.md) \| [Next (1.4 Strings)](04_Strings.md)
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# 1.3 Numbers
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This section discusses mathematical calculations.
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### Types of Numbers
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Python has 4 types of numbers:
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* Booleans
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* Integers
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* Floating point
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* Complex (imaginary numbers)
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### Booleans (bool)
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Booleans have two values: `True`, `False`.
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```python
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a = True
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b = False
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```
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Numerically, they're evaluated as integers with value `1`, `0`.
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```python
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c = 4 + True # 5
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d = False
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if d == 0:
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print('d is False')
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```
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*But, don't write code like that. It would be odd.*
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### Integers (int)
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Signed values of arbitrary size and base:
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```python
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a = 37
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b = -299392993727716627377128481812241231
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c = 0x7fa8 # Hexadecimal
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d = 0o253 # Octal
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e = 0b10001111 # Binary
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```
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Common operations:
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```
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x + y Add
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x - y Subtract
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x * y Multiply
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x / y Divide (produces a float)
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x // y Floor Divide (produces an integer)
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x % y Modulo (remainder)
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x ** y Power
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x << n Bit shift left
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x >> n Bit shift right
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x & y Bit-wise AND
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x | y Bit-wise OR
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x ^ y Bit-wise XOR
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~x Bit-wise NOT
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abs(x) Absolute value
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```
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### Floating point (float)
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Use a decimal or exponential notation to specify a floating point value:
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```python
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a = 37.45
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b = 4e5 # 4 x 10**5 or 400,000
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c = -1.345e-10
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```
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Floats are represented as double precision using the native CPU representation [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754).
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This is the same as the `double` type in the programming language C.
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> 17 digits or precision
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> Exponent from -308 to 308
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Be aware that floating point numbers are inexact when representing decimals.
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```python
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>>> a = 2.1 + 4.2
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>>> a == 6.3
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False
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>>> a
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6.300000000000001
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>>>
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```
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This is **not a Python issue**, but the underlying floating point hardware on the CPU.
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Common Operations:
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```
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x + y Add
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x - y Subtract
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x * y Multiply
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x / y Divide
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x // y Floor Divide
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x % y Modulo
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x ** y Power
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abs(x) Absolute Value
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```
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Theses are the same operators as Integers, except for the bit-wise operators.
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Additional math functions are found in the `math` module.
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```python
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import math
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a = math.sqrt(x)
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b = math.sin(x)
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c = math.cos(x)
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d = math.tan(x)
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e = math.log(x)
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```
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### Comparisons
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The following comparison / relational operators work with numbers:
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```
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x < y Less than
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x <= y Less than or equal
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x > y Greater than
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x >= y Greater than or equal
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x == y Equal to
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x != y Not equal to
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```
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You can form more complex boolean expressions using
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`and`, `or`, `not`
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Here are a few examples:
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```python
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if b >= a and b <= c:
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print('b is between a and c')
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if not (b < a or b > c):
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print('b is still between a and c')
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```
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### Converting Numbers
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The type name can be used to convert values:
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```python
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a = int(x) # Convert x to integer
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b = float(x) # Convert x to float
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```
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Try it out.
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```python
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>>> a = 3.14159
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>>> int(a)
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3
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>>> b = '3.14159' # It also works with strings containing numbers
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>>> float(b)
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3.14159
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>>>
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```
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## Exercises
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Reminder: These exercises assume you are working in the `practical-python/Work` directory. Look
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for the file `mortgage.py`.
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### Exercise 1.7: Dave's mortgage
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Dave has decided to take out a 30-year fixed rate mortgage of $500,000
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with Guido’s Mortgage, Stock Investment, and Bitcoin trading
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corporation. The interest rate is 5% and the monthly payment is
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$2684.11.
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Here is a program that calculates the total amount that Dave will have
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to pay over the life of the mortgage:
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```python
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# mortgage.py
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principal = 500000.0
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rate = 0.05
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payment = 2684.11
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total_paid = 0.0
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while principal > 0:
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principal = principal * (1+rate/12) - payment
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total_paid = total_paid + payment
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print('Total paid', total_paid)
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```
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Enter this program and run it. You should get an answer of `966,279.6`.
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### Exercise 1.8: Extra payments
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Suppose Dave pays an extra $1000/month for the first 12 months of the mortgage?
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Modify the program to incorporate this extra payment and have it print the total amount paid along with the number of months required.
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When you run the new program, it should report a total payment of `929,965.62` over 342 months.
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### Exercise 1.9: Making an Extra Payment Calculator
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Modify the program so that extra payment information can be more generally handled.
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Make it so that the user can set these variables:
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```python
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extra_payment_start_month = 60
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extra_payment_end_month = 108
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extra_payment = 1000
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```
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Make the program look at these variables and calculate the total paid appropriately.
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How much will Dave pay if he pays an extra $1000/month for 4 years starting in year 5 of the mortgage?
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### Exercise 1.10: Making a table
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Modify the program to print out a table showing the month, total paid so far, and the remaining principal.
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The output should look something like this:
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```bash
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1 2684.11 499399.22
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2 5368.22 498795.94
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3 8052.33 498190.15
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4 10736.44 497581.83
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5 13420.55 496970.98
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...
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308 875705.88 674.44
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309 878389.99 -2006.86
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Total paid 878389.99
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Months 309
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```
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### Exercise 1.11: Bonus
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While you’re at it, fix the program to correct the for overpayment that occurs in the last month.
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### Exercise 1.12: A Mystery
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`int()` and `float()` can be used to convert numbers. For example,
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```python
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>>> int("123")
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123
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>>> float("1.23")
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1.23
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>>>
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```
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With that in mind, can you explain this behavior?
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```python
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>>> bool("False")
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True
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>>>
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```
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[Contents](../Contents.md) \| [Previous (1.2 A First Program)](02_Hello_world.md) \| [Next (1.4 Strings)](04_Strings.md)
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