Question

Question: Define the magnitude of a number as the location of the decimal point from the left of the number (that is, if a number has 4 digits followed by the decimal point, it will have a magnitude of 4). 100 would then have a magnitude of 3 and 88,888.888 would have a magnitude of 5. A partial recursive method is given below to compute a positive int parameter's

Define the magnitude of a number as the location of the decimal point from the left of the number (that is, if a number has 4 digits followed by the decimal point, it will have a magnitude of 4). 100 would then have a magnitude of 3 and 88,888.888 would have a magnitude of 5. A partial recursive method is given below to compute a positive int parameter's magnitude. Which answer below is needed to complete the method?

O magnitude(x - 1) + 10;
O magnitude(x / 10) * 2;
O magnitude(x / 10) + 1;
O magnitude(x - 10) + 1;
O magnitude(x / 10) + 10;

Answer 1

The correct completion for the method to compute the magnitude (total number of digits before the decimal point for whole numbers) is 'magnitude(x / 10) + 1'. This option correctly counts down the number of digits in the number until it reaches 0.

Step-by-step explanation:

The magnitude of a number, in the context of the given student question, refers to the position of the decimal point from the left side of a whole number which is similar to the concept of order of magnitude in scientific notation. However, it appears there is a misinterpretation in the question where 'magnitude' is confused with 'order of magnitude'.

While magnitude here algorithmically refers to the total number of digits before the decimal point (for whole numbers), the order of magnitude refers to the power of 10 that closely approximates a number and is determined through scientific notation or base-10 logarithms.

Given the recursive method to compute the magnitude, the correct completion for the method is magnitude(x / 10) + 1. This statement works by successively dividing the number by 10 (removing one digit from the end) until it reaches a point where no digits are left before the decimal point, adding 1 each time a digit is removed (indicating a reduction in magnitude by one).