Number types

When working with math operations in your code, your coders need to know about the different types of numbers they can use. Each number type is suited to a different purpose:

• Integers are negative numbers, zero, or positive numbers. They don’t have decimal place digits. Integers can be used for a variety of purposes. They can indicate position on a number line or a coordinate grid. They can be used to count things. They can be used to count the number of likes on a YouTube video! In programming languages that require a number type to be declared, the code for an integer is typically int.
• Decimals are numbers that have a decimal point and digits after the decimal. They can be negative, zero, or positive in value. Decimals are used for number quantities that require precision. Weight, salaries, land acreage, and clocks measuring elapsed times at sporting events. In programming languages that require a number type to be declared, the code for a decimal number is typically double.

See Chapter 7 for more information on number typing.

Dramatizing math

To understand mathematics and math operations in coding, try some math activities, unplugged. Play a board game with your coder. (See Figure 8-2.) Almost all board games involve rolling dice, summing their values, and moving a marker around the board to build counting skills. Playing dominoes does as well. Games such as Monopoly also involve buying and selling and can help your coder in working with currency. Card games such as twenty-one and Old Maid help players build skills in probability as they try to determine the chances on drawing the cards they want, or don't want. In this age of apps and video games, you may also find that you and your coder enjoy a little game time that doesn’t involve screen time!

Using pseudocode

Programming languages follow the same general rules with regard to performing math operations. Table 8-1 shows general pseudocode for these operations with an example of integers and decimals.

Using Scratch

Scratch, similar to other block-based coding languages, has simple blocks that support basic math operations, as shown in Figure 8-3. Scratch supports adding integers and decimals.

Scratch also supports combining simple math operations. Figure 8-4 shows a set of blocks that adds four numbers together.

One thing to point out to young coders when they're writing in a block-based language such as Scratch is that to add four numbers, you only need three add blocks.

Using Python

Basic math operations in Python look very similar to pseudocode. This makes sense, considering Python aimed to be a language that was approachable and familiar for humans (see the sidebar about Guido van Rossum in Chapter 3). Python supports math operations for integers and decimals, although in Python a decimal is called a float. For adding, subtracting, multiplying, and dividing, you would follow the pseudocode (refer to Table 8-1). For example, addition in Python for integers and floats is like this:

3 + 5

2.78 + 1.2 + 5.6

This is actually true for most text-based languages. For example, that’s exactly how you would add two numbers in Java and JavaScript as well!

Using pseudocode

Just like the basic math operations in the previous section, more advanced math operations can support integers and decimals in almost all programming languages. Table 8-2 shows examples of how you might write code for changing the sign of a number, and for other advanced math operations. It also shows how to write pseudocode when using variables in advanced math operations.

Turn to Chapter 7 to find out how to declare a variable and how to give a variable a new name.

Using Scratch

Scratch provides users with a number of math operations beyond the basic four. Figure 8-5 shows how to change the sign of a number: multiply the number by negative one (-1). In this way, a positive number becomes negative, and a negative number becomes positive.

Finding an exponent in Scratch can also be a bit tricky. There isn't a simple block for number1^number2. There are two blocks for exponent functions, shown in Figure 8-6, but are specific to e^number1 and 10^number1. These blocks can be found under Operations (see Figure 8-7). To write the function for number1^number2, you basically have to write all the multiplications, also shown in Figure 8-6.

Scratch makes a lot of the other advanced math operations very easy! Finding the absolute value and square root of a value uses one block, which can be found under the Operations category. Figure 8-7 shows the block and all the choices you have for it. Absolute value is represented as abs and square root is represented as sqrt. The block starts as sqrt.

Combining variables with math operations in Scratch is really easy. Basically, anywhere there is a circular opening you can either type a number or drag in a variable. For example, Figure 8-8 shows some of the math operations throughout this chapter using variables.

Using Python

Negating a number, finding the exponent, absolute value, and square root in Python are all straightforward. You can perform all three operations on integer or decimal (float) numbers.

Negating a number in Python pretty much only makes sense if you're trying to negate the value of a variable; otherwise you would just use the positive or negative number. Although, you can still negate a number directly, just add parenthesis for clarity:

-(number1)

Examples

-(5)

-(-8.99)

Exponents are pretty much the same as the basic math operations (like adding) and use a special symbol:

number1 ** number2

Examples:

3 ** 5

2.78 ** 1.2

Getting the absolute value of a number in Python requires you to use a function. Functions in Python (and other text-based languages) are special commands or subprograms that you call in your code. Typically, you pass the function a parameter (a value for the function to use in a computation) and the function returns an output value to you. You might have already encountered some functions if you worked through earlier chapters in this book. For example, a function in JavaScript from Chapter 5 is:

getXPosition("character");

Here’s the Python code for absolute value:

abs(number1)

Examples are

abs(-7)

abs(8.9)

Finding the square root of a number is even a little more complicated than finding the absolute value when coding in Python. First, you have to import a Math library so that Python knows how to evaluate this method (which is another type of subprogram you can call in Python).

import math

math.sqrt(number1)

Examples are

import math

math.sqrt(16)

math.sqrt(99.89)

For additional information on subprograms your coder can write in his code, see Chapter 12.

Finally, using variables in more advanced Python math operations is very similar to using them in Scratch — basically you replace numbers with variables! A couple examples are here:

Finding the absolute value with variables:

costOfTable1 = 66.89

costOfTable2 = 90.54

differenceInCost = abs(66.89 – 90.54)

Finding the square root with variables:

areaOfSquareRoom = 196

lengthOfOneWall = math.sqrt(areaOfSquareRoom)

Using pseudocode

Mod in pseudocode is often represented with the % symbol, because that is most commonly used in text-based languages like Python and Java.

number1 % number2

Examples are

30 % 7

6.89 % 5.9

Using Scratch

In Scratch, you can find a mod block under the Operators category. For example, Figure 8-10 shows the mod block evaluating 9 mod 8, which equals 1.

Using Python

In Python, the mod operator is very similar to the basic math operations such as adding, subtracting, multiplying, and dividing. You simply use the % symbol between the numbers. It's exactly like the pseudocode examples for both integers and decimals.

Using Scratch

Because Scratch doesn’t have a parenthesis symbol, it behaves differently when it comes to the order of operations. Basically, each individual block is evaluated first because each block is basically representing an operation within parentheses. For example, Figure 8-11 shows a compound math operation using addition and division. The order of operations for Figure 8-11 written in pseudocode is:

8 + 6

10 + 14

24 / 3

aveScore = 8

It can also be viewed all in one line like this:

aveScore = (10 + (8 + 6)) / 3

Using Python

Python follows the PEMDAS rule, although two operations aren’t accounted for in PEMDAS; negation and mod. Negation (N) comes after parenthesis, but before exponents: PNEMDAS. Mod (m) is at the same level as multiplication and division: PNEMDmAS. Some examples of how Python would evaluate compounded math operations are here:

Compound math operation without parenthesis:

print( 5 * 9 % 8 + 9 / 3 )

8

The steps that Python takes are:

5 * 9 = 45

45 % 8 = 5

9 / 3 = 3

5 + 3 = 8

Compound math operation with parentheses result in a different computation:

print( 5 * ((9 % 8) + 9) / 3 )

16

The steps that Python takes are:

9 % 8 = 1

1 + 9 = 10

5 * 10 = 50

50 / 3 = 16

Rounding via casting in Java

In a typed programming language, where you specify what type the values are that you’re using, you can explicitly cast either the number in the operator, or the result to an integer or a decimal. Casting means to tell the computer explicitly what type you want a value to be, instead of letting the computer determine what type a value is based on its properties. Notice in the following examples that programming languages typically round down, regardless of how close to the next integer the decimal is. For example, in Java you might have the following:

(int)60.8 + 7;

67

int sum = (int)(89.333 + 1.555);

sum = 90

int sum = (int)(89.3 + 1.7);

sum = 91

double quotient = (double)8 / 3;

quotient = 2.6666666666666665

double quotient = (int)8.4 / 3;

quotient = 2.0

When adding precision, you can perform explicit or implicit casting. Implicit casting is when the programming language adds precision to numbers based on all the numbers being used in the operation. Explicit casting is described in the section coming up.

double quotient = 8 / 3;

quotient = 2.0

double quotient = 8.0 / 3;

quotient = 2.6666666666666665

Rounding decimals to integers via methods

Although rounding occurs often between integers and decimals during math operations, most programming languages also have a rounding method that can be used to explicitly round decimals to the nearest integer. This is the same in standard math operations:

5.5 = 6

5.4999 = 5

Figure 8-12 shows a few examples of rounding in Scratch.

The following table shows a couple rounding examples in both Python and Java:

Some programming languages even have functions that let you round to a certain decimal! For example, Python's round function can be extended to include a second parameter where you specify how many digits after the decimal you want the number rounded to:

round(5.5985, 2)

5.60

round(5.46732, 4)

5.4673

Using pseudocode

When trying to find a random number between two numbers, it’s important to know whether you’re including the two numbers that are your boundaries, or not including them. For example, a random number between 1 and 5 inclusive could be 1, 2, 3, 4, or 5. While a random number between 1 and 5 exclusive could only be 2, 3, or 4. You might also want to decide to include the first number, but not the last. For example, a random number between 1 and 5 including 1 but excluding 5 could be 1, 2, 3, or 4. To specify this with pseudocode, you would typically use the symbol [ to denote inclusivity of the number and ( to denote exclusivity.

The functions (with examples) needed to choose a random number are:

Using Scratch

Scratch provides an easy to use the random block under the Operators category, as shown in Figure 8-13. Scratch's random block is inclusive. The random block returns an integer if both values given are integers, and returns a decimal even if one of the numbers is a decimal. The precision of the decimal matches that of the most precise parameter given.

Using Python

To use the random function in Python, you have to first import the random library. You can then call the randint function to find a random integer or the uniform function to find a random float (decimal). Both the randint and uniform functions are inclusive.

Functions (with examples) to choose a random number are: