Number tools: round, abs, divmod, min and max

What you will be able to do

After this lesson you can

• round a number to the places that you need,
• tell the difference between round() and int(),
• find the size of a difference with abs(), and
• use min(), max() and divmod() to write short programs.

Tools that are always ready

You met print() already. It is a function: a ready-made helper with a name and brackets. Python has many functions for numbers. They are always ready, and you do not have to install anything. Here are the five that you will use most.

round() and int() are not the same

A note on round(2.5): it gives 2, and not 3. Python rounds a number that is exactly in the middle to the nearest even whole number. This is also done in science, because over many numbers it makes less error. You do not need to worry about it, but now you will not be surprised.

Try 2.5 and 3.5 as well. At exactly a half, Python rounds to the even neighbour.

Putting the tools together

A teacher has the marks of five students: 72, 85, 91, 64, 78. A short program can find the highest, the lowest, and the gap.

• highest = max(72, 85, 91, 64, 78) is 91.
• lowest = min(72, 85, 91, 64, 78) is 64.
• gap = highest - lowest is 27.
• The average is (72 + 85 + 91 + 64 + 78) / 5, which is 78.0.

When you show a result, think about how many digits the reader needs. A mark of 78.0 is easier to read than 78.00000000001.

Common mistakes

• Using int() when you want to round. int(2.9) is 2. Use round(2.9), which is 3.
• Forgetting that round() gives an int with one number and a float with two. round(2.6) is 3, and round(2.6, 1) is 2.6.
• Taking abs of a sum. abs(-3 + 5) is 2, but abs(-3) + abs(5) is 8. The brackets decide.
• Writing min(3, 4, 5 without the closing bracket.
• Forgetting the comma between the numbers in max(3 4 5).

Practice

Start with two quick questions. Each New numbers gives you a fresh one, so you can practise as long as you like.

Then the labs and the problems:

1. Warm-up. Open the lab Round and compare. Use round() and abs() on a few numbers. The checker confirms your answers.
2. Build. Open the problem Round and absolute value, and then write a program that finds the gap between the biggest and the smallest of five numbers.
3. Stretch. Do the lab Take a number apart. Use divmod() to take 472 apart into hundreds, tens and ones.

Remember these

• round(x, n) rounds to n places. int(x) cuts off the decimal part.
• abs(x) is the size of x. min() and max() pick the smallest and the biggest.
• divmod(a, b) gives the quotient and the remainder together.
• Round a result before you show it to a reader.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What are round(7.46, 1) and int(7.46)?

2. What is abs(3 - 10)?

3. How can you get quotient and remainder of 100 / 7 with one line?

4. What is max(5, -9, 2)?