Question

Explain what happens when a Java program attempts to divide one integer by another. What happens to the fractional part of the calculation? How can you avoid that outcome?

Short answer

Dividing one integer by another in Java results in integer division, where the fractional part is discarded. To retain the fractional part, cast one or both operands to a float or double before the division.

Step-by-step solution

Understanding Integer Division in Java

In Java, when one integer is divided by another, the operation is called integer division. This operation discards any fractional part of the calculation and results in a whole number. For example, when dividing 5 by 2, the expected mathematical result is 2.5, but Java will produce a result of 2.

Consequences of Integer Division

Due to the integer division behavior, any fractional part that would result from the division is simply truncated. This means it is not rounded; it is discarded entirely. Thus, arithmetic operations that involve division might not behave as some programmers coming from other languages might expect.

Avoiding Integer Division

To avoid losing the fractional part, one or both of the operands in the division must be cast to a floating-point type, such as float or double. For example, to get the full decimal result of 5 divided by 2, you could write the division as (double) 5 / 2, which would produce a result of 2.5.

Key concepts

Integer Division

When learning to program in Java, understanding how the language handles arithmetic operations is crucial, especially when it comes to division with integers. Suppose you're presented with a simple division problem where you need to divide one integer by another, say dividing 7 by 3. You might expect the answer to be a decimal number since 7 isn't evenly divisible by 3. However, in Java, the operation will yield 2, not 2.3333... as one might typically expect. Why does this happen?

Java performs what's known as integer division when both operands are integers. In integer division, the result is always rounded down to the closest integer that's smaller than or equal to the exact result. This 'rounding down' is also called truncation. The fractional part is entirely discarded without rounding. So, if this truncation isn't what you want, the key is to involve floating-point arithmetic in your operations, which leads to our next core concept.

Floating-point Arithmetic

To understand why you might needed to switch to floating-point arithmetic, let's revisit our previous example where we divided 7 by 3 and got 2 using integer division. If we intend to preserve the fractional component of the division, we need to use floating-point numbers, such as 'float' or 'double'. These types are capable of holding decimal values and can give you the precision you need for arithmetic operations.

Floating-point arithmetic allows calculations to result in a number with a decimal point, carrying the significant digits after it. For instance, if we cast one of the integers to a double before the division - say (double) 7 / 3 - Java no longer sees it as an integer division but as floating-point arithmetic, and it will return 2.3333... as expected.

This type of arithmetic is subject to rounding errors because of the way floating-point numbers are represented in memory, which is something to be aware of as it can affect the accuracy of your calculations if not handled correctly.

Type Casting

When a Java program demands more precision than integer division can provide, or when we need to mix different types in arithmetic operations, type casting comes into play. Type casting is a way of converting a variable from one data type to another. In the context of Java arithmetic, casting is often used to convert integers to floating-point numbers before performing division, thus ensuring that the result includes any fractional part.

Let's delve further using our division example of 5 by 2. To get a result with a decimal point, either one of the integers (or both) needs to be cast to a float or double like this: (double) 5 / 2. What happens here is called explicit casting, where we manually convert the integer 5 into a double before executing the division, allowing us to preserve the decimal fraction and get the full result of 2.5.

Casting is a powerful tool that can also lead to information loss if not used properly, like when casting a floating-point number to an integer, which will cause truncation of the decimal part. It's important to use casting with care to avoid such unintended results.