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c) Use the methods developed in parts (a) and (b) to write a method
displayDigits
that
receives an integer between
1
and
99999
and displays it as a sequence of digits, separating
each pair of digits by two spaces. For example, the integer
4562
should appear as
4 5 6 2
Incorporate the methods into an application that inputs an integer and calls
display-
Digits
by passing the method the integer entered. Display the results.
6.22
(Temperature Conversions)
Implement the following integer methods:
a) Method
celsius
returns the Celsius equivalent of a Fahrenheit temperature, using the
calculation
celsius =
5.0
/
9.0
* (fahrenheit -
32
);
b) Method
fahrenheit
returns the Fahrenheit equivalent of a Celsius temperature, using
the calculation
fahrenheit =
9.0
/
5.0
* celsius +
32
;
c) Use the methods from parts (a) and (b) to write an application that enables the user ei-
ther to enter a Fahrenheit temperature and display the Celsius equivalent or to enter a
Celsius temperature and display the Fahrenheit equivalent.
6.23
(Find the Minimum)
Write a method
minimum3
that returns the smallest of three floating-
point numbers. Use the
Math.min
method to implement
minimum3
. Incorporate the method into an
application that reads three values from the user, determines the smallest value and displays the re-
sult.
6.24
(Perfect Numbers)
An integer number is said to be a
perfect number
if its factors, including
1 (but not the number itself), sum to the number. For example, 6 is a perfect number, because 6 =
1 + 2 + 3. Write a method
isPerfect
that determines whether parameter
number
is a perfect number.
Use this method in an application that displays all the perfect numbers between 1 and 1000. Display
the factors of each perfect number to confirm that the number is indeed perfect. Challenge the com-
puting power of your computer by testing numbers much larger than 1000. Display the results.
6.25
(Prime Numbers)
A positive integer is
prime
if it's divisible by only 1 and itself. For example,
2, 3, 5 and 7 are prime, but 4, 6, 8 and 9 are not. The number 1, by definition, is not prime.
a) Write a method that determines whether a number is prime.
b) Use this method in an application that determines and displays all the prime numbers
less than 10,000. How many numbers up to 10,000 do you have to test to ensure that
you've found all the primes?
c) Initially, you might think that
n
/2 is the upper limit for which you must test to see
whether a number
n
is prime, but you need only go as high as the square root of
n
. Re-
write the program, and run it both ways.
6.26
(Reversing Digits)
Write a method that takes an integer value and returns the number with
its digits reversed. For example, given the number 7631, the method should return 1367. Incorpo-
rate the method into an application that reads a value from the user and displays the result.
6.27
(Greatest Common Divisor)
The
greatest common divisor
(
GCD
) of two integers is the largest
integer that evenly divides each of the two numbers. Write a method
gcd
that returns the greatest
common divisor of two integers. [
Hint:
You might want to use Euclid's algorithm. You can find
information about it at
en.wikipedia.org/wiki/Euclidean_algorithm
.] Incorporate the method
into an application that reads two values from the user and displays the result.
6.28
Write a method
qualityPoints
that inputs a student's average and returns
4
if it's 90-100,
3
if 80-89,
2
if 70-79,
1
if 60-69 and
0
if lower than 60. Incorporate the method into an application
that reads a value from the user and displays the result.
