Question

In the array declaration double score[5] state the following: a. The array name b. The base type c. The declared size of the array d. The range of values that an index for this array can have e. One of the indexed variables (or elements) of this array

Short answer

Answer: The array name is "score", with a base type of "double" and a declared size of 5. The index range for this array is 0 to 4 (inclusive). An example of an indexed variable within this array is "score[2]".

Step-by-step solution

a. The array name

The array name is "score".

b. The base type

The base type of the array is "double", which means this array can store decimal numbers (floating-point numbers).

c. The declared size of the array

The declared size of the array is 5, as indicated by the number within the brackets [5]. This means the array can store up to 5 elements.

d. The range of values that an index for this array can have

The range of valid indices for this array is from 0 to 4 (inclusive), since we're using zero-based indexing.

e. One of the indexed variables (or elements) of this array

One of the indexed variables (or elements) of this array could be "score[2]". This would refer to the third element in the array, as the first element has an index of 0.

Key concepts

Array Base Type

When declaring an array in C++, specifying the base type is crucial as it defines the type of elements that the array will store. In the example given, double score[5], the base type is double, which means each element of the array can hold a floating-point number. This is a very specific kind of number that allows for the representation of decimals, which are critically important in applications that require precision, such as scientific calculations.

Floating-point numbers come in different sizes: float and double, where double has double the precision of float. Selecting the appropriate base type affects both the precision of the calculations and the amount of memory the array will consume. For example, if precision is not crucial, one might choose float to save memory.

Array Size

The array size in C++ denotes how many elements an array can hold. It is designated in the array declaration by an integer within square brackets. In double score[5], the number 5 indicates the size of the array, declaring that the array score can store up to five elements.

It's essential to note that the array size must be a compile-time constant in C++, meaning its value must be known when the program is compiled. In practical use, this helps to prevent errors such as buffer overflows, which can lead to unintended program behavior. Choosing an appropriate size for the array is a trade-off between memory usage and flexibility, as allocating more space than needed can waste memory, while too little space may limit functionality.

Zero-Based Indexing

C++ arrays use zero-based indexing, which means the index of the first element is 0 rather than 1. This convention is used throughout many programming languages and requires a slight mental adjustment for those new to coding.

In the array double score[5], indexing starts at 0 and goes up to 4, making for a total of 5 elements corresponding to the declared size. Here's how the indices map to elements in the array:

• score[0] - First element
• score[1] - Second element
• score[2] - Third element
• score[3] - Fourth element
• score[4] - Fifth and last element

Understanding zero-based indexing is essential for navigating arrays correctly and avoiding off-by-one errors that can lead to bugs in program logic.

Floating-Point Numbers

In the context of arrays, when we declare an array with a base type of double, as in double score[5], we are setting aside space for floating-point numbers. Floating-point numbers represent real numbers with a decimal point and encompass a vast range, from extremely small to very large numbers.

The term 'floating-point' comes from the way these numbers are represented internally, with a 'floating' decimal point that moves around to accurately depict the magnitude and precision of the number. For instance, double allows for about 15 decimal digits of precision, while float allows for about 7. This precision is pivotal when working with computations that require a high degree of accuracy, such as financial calculations or complex scientific simulations. Always remember to consider the needs of your application before choosing between float and double data types.