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David Beazley
2020-05-26 11:40:09 -05:00
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Notes/01_Introduction/03_Numbers.md
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@@ -1,7 +1,5 @@
# 1.3 Numbers
This section covers some basics of performing mathematical calculations in Python.
### Types of Numbers
Python has 4 types of numbers:
@@ -11,7 +9,7 @@ Python has 4 types of numbers:
* Floating point
* Complex (imaginary numbers)
### Booleans
### Booleans (bool)
Booleans have two values: `True`, `False`.
@@ -29,9 +27,9 @@ if d == 0:
print('d is False')
```
*Don't do that, it would be odd.*
*Don't write code like that. It would be odd.*
### Integers
### Integers (int)
Signed values of arbitrary size and base:
@@ -62,26 +60,6 @@ x ^ y Bit-wise XOR
abs(x) Absolute value
```
### Comparisons
The following comparison / relational operators work with numbers:
`<`, `>`, `<=` `>=`, `==`, `!=`
You can form more complex boolean expressions using
`and`, `or`, `not`
Here are a few examples:
```python
if b >= a and b <= c:
print('b is between a and c')
if not (b < a or b > c):
print('b is still between a and c')
```
### Floating point (float)
Use a decimal or exponential notation to specify a floating point value:
@@ -136,6 +114,34 @@ d = math.tan(x)
e = math.log(x)
```
### Comparisons
The following comparison / relational operators work with numbers:
```
x < y Less than
x <= y Less than or equal
x > y Greater than
x >= y Greater than or equal
x == y Equal to
x != y Not equal to
```
You can form more complex boolean expressions using
`and`, `or`, `not`
Here are a few examples:
```python
if b >= a and b <= c:
print('b is between a and c')
if not (b < a or b > c):
print('b is still between a and c')
```
### Converting Numbers
The type name can be used to convert values:
@@ -159,7 +165,7 @@ Try it out.
## Exercises
### (a) Dave's mortgage
### Exercise 1.7: Dave's mortgage
Dave has decided to take out a 30-year fixed rate mortgage of $500,000 with Guido’s Mortgage, Stock Investment, and Bitcoin trading corporation.
The interest rate is 5% and the monthly payment is $2684.11.
@@ -183,7 +189,7 @@ print('Total paid', total_paid)
Enter this program and run it. You should get an answer of `966,279.6`.
### (b) Extra payments
### Exercise 1.8: Extra payments
Suppose Dave pays an extra $1000/month for the first 12 months of the mortgage?
@@ -191,7 +197,7 @@ Modify the program to incorporate this extra payment and have it print the total
When you run the new program, it should report a total payment of `929,965.62` over 342 months.
### (c) Making an Extra Payment Calculator
### Exercise 1.9: Making an Extra Payment Calculator
Modify the program so that extra payment information can be more generally handled.
Make it so that the user can set these variables:
@@ -206,7 +212,7 @@ Make the program look at these variables and calculate the total paid appropriat
How much will Dave pay if he pays an extra $1000/month for 4 years starting in year 5 of the mortgage?
### (d) Making a table
### Exercise 1.10: Making a table
Modify the program to print out a table showing the month, total paid so far, and the remaining principal.
The output should look something like this:
@@ -224,8 +230,28 @@ Total paid 878389.99
Months 309
```
### (e) Bonus
### Exercise 1.11: Bonus
While you’re at it, fix the program to correct the for overpayment that occurs in the last month.
### Exercise 1.12: A Mystery
`int()` and `float()` can be used to convert numbers. For example,
```pycon
>>> int("123")
123
>>> float("1.23")
1.23
>>>
```
With that in mind, can you explain this behavior?
```pycon
>>> bool("False")
True
>>>
```
[Contents](../Contents) \| [Previous (1.2 A First Program)](02_Hello_world) \| [Next (1.4 Strings)](04_Strings)