1.2 Python Arithmetic Operators

To Write Your Third Python Code

$$7\times 95$$

1. Click + Code on a notebook to add a code cell
2. Type 7*95
3. Press the play button to execute the code
4. 665 is the result

To Save Your Colab Notebook

Watch demo video

1. Click Untitled.ipynb at the top of the notebook
2. Delete the title and replace it by typing python1
3. Press the enter key
4. The file python1 is now saved in your Google Drive
5. Click File and then Save
6. Close your browser

To Open Your python1 Notebook

1. Click this link http://colab.research.google.com#create=true or go to your Google Drive.
2. Click python1 from the list on the pop-up window
3. The notebook will open

OR click the File menu then Open Notebook

Note: For the examples below:

1. Add a new code cell on a Colab notebook
2. Type the code based on the statement of the example
3. Execute the code

Example: Multiply $5\times 6$

5*6

30

Example: Divide $10÷3$

10/3

3.3333333333333335

Example: Exponentiate $5^2$

5**2

25

Example: Add and then divide

$$(2+3+5+4)÷4$$

(2+3+5+4)/4

3.5

Note: If you want to add the numbers in the numerator $2+3+5+4$ first and then divide it by the denominator, $4$, you will need to save the sum of the numerator first. We will cover how to save the sum in a variable name in the next section.

Example: Add $\frac{1}{2}+\frac{1}{3}+\frac{2}{5}+10$

1/2+1/3+2/5+10

11.233333333333334

Note: Adding parentheses to the fractions makes it clearer (see below)

(1/2)+(1/3)+(2/5)+10

11.233333333333334

Example: Perform the operations $6÷3\times 7-6.7+3.5$

6/3*7-6.7+3.5

10.8

Example: Perform the operations $43+(8-5{)}^3÷(34-5^2)$

43+(8-5)**3/(34-5**2)

46.0

Example: Perform the operation $13\frac{1}{2}+2.4\times {1.4}^2$

13+1/2+2.4*1.4**2

18.204

Note: Radicals in Rational Exponents Watch demo video

If $x$ is a real number, $a$ is integer and $b$ is positive integer then

$$\sqrt[b]{x^a}=x^{\frac{a}{b}}$$

For example:

$$\sqrt{8}=8^{1/2}$$

$$\sqrt[3]{8}=8^{1/3}$$

$$\sqrt[4]{8^3}=8^{3/4}$$

Example: Evaluate $\sqrt{7}=7^{1/2}$

7**(1/2)

2.6457513110645907

7**.5

2.6457513110645907

Note: 1/2 =.5

Example: Evaluate $\sqrt[3]{7}$

$$\sqrt[3]{7}=7^{1/3}$$

7**(1/3)

1.912931182772389

Example: Find $\sqrt{5^2-4}$

Note: $\sqrt{5^2-4}=(5^2-4{)}^{1/2}$

(5**2-4)**(1/2)

4.58257569495584

Example: Follow standard math order of operations to evaluate:

$$\sqrt{5^2-4\times 2\times (-3)}$$

Note: $$\sqrt{5^2-4\times 2\times (-3)}=(5^2-4\times 2\times (-3){)}^{1/2}$$

(5**2-4*2*(-3))**(1/2)

7.0

Example: Follow standard math order of operations to evaluate:

$$-2+\sqrt{5^2-4\times 2\times (-3)}$$

Caution: Everything under the square root is inside a parenthesis raised to 1/2. That is $5^2-4\times 2\times (-3)$ is raided to $1/2$. You can do this in two steps using variables in the next section

-2+(5**2-4*2*(-3))**(1/2)

5.0

Example: Evaluate:

$$\frac{-2+\sqrt{5^2-4\times 2\times (-3)}}{2\times 2}$$

Notice how paired parentheses are used to enforce order of operations.

(-2+(5**2-4*2*(-3))**(1/2))/(2*2)

1.25

Scientific Notations

Example: Divide $\frac{1}{186000}$

1/186000

5.376344086021505e-06

Note: The Python output 5.376344086021505e-06 is in scientific notation. $$5.376344086021505e-06=5.376344086021505\times {10}^{-6}$$

Adapted from Python for Introductory Statistics, by Simon Aman (Truman College, City Colleges of Chicago), licensed under CC BY 4.0. Changes were made: reformatted as an accessible XYZ web edition with live in-browser code cells. License: CC-BY-4.0.