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Questions and Answers
What is the core property that defines a Caprica number?
What is the core property that defines a Caprica number?
- Its square can be split into two parts that sum to the original number. (correct)
- It equals the sum of all its factors.
- It is a prime number within a given range.
- Its digits sum to a perfect square.
In the Java code implementation, why is it necessary to convert the number to a string?
In the Java code implementation, why is it necessary to convert the number to a string?
- To convert the number to its binary representation.
- To validate that the number contains only numeric characters.
- To determine the number of digits in the number. (correct)
- To perform mathematical operations more efficiently.
What is the purpose of the Math.pow(10, l) function in the context of identifying Caprica numbers?
What is the purpose of the Math.pow(10, l) function in the context of identifying Caprica numbers?
- To calculate the square root of the number.
- To round the number to the nearest power of 10.
- To calculate 10 raised to the power of the number of digits, used to split the squared number. (correct)
- To determine the factorial of the number.
What part of the Caprica number verification process involves calculating a quotient?
What part of the Caprica number verification process involves calculating a quotient?
What is the role of the isCaprica method in the provided Java code?
What is the role of the isCaprica method in the provided Java code?
Why is the isCaprica method invoked without creating an object of the class?
Why is the isCaprica method invoked without creating an object of the class?
What is the primary function of the main method in the context of the Caprica number program?
What is the primary function of the main method in the context of the Caprica number program?
If a number's square is '1681' and it is determined that the right side is '81' and the left side is '16', what should the next step be to check if the original number is a Caprica number?
If a number's square is '1681' and it is determined that the right side is '81' and the left side is '16', what should the next step be to check if the original number is a Caprica number?
Within the range of 1 to 100, which of the following sets contains only Caprica numbers?
Within the range of 1 to 100, which of the following sets contains only Caprica numbers?
To verify that 99 is a Caprica number, what steps should be followed after calculating that 99 squared equals 9801?
To verify that 99 is a Caprica number, what steps should be followed after calculating that 99 squared equals 9801?
Flashcards
Caprica Number
Caprica Number
A number whose square can be split into two parts that sum to the original number.
Example of Caprica Number
Example of Caprica Number
45 is a Caprica number because 45*45 = 2025 and 20 + 25 = 45.
String Conversion Purpose
String Conversion Purpose
Converts the number to a string to determine the number of digits for splitting the squared value.
Finding Right-Side Digits
Finding Right-Side Digits
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Finding Left-Side Digits
Finding Left-Side Digits
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isCaprica Method
isCaprica Method
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Main Method Purpose
Main Method Purpose
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Caprica Numbers Example
Caprica Numbers Example
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Verification of Caprica Number
Verification of Caprica Number
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Study Notes
Caprica Number Definition
- A Caprica number's square can be split.
- The sum of these parts equals the original number.
Example of a Caprica Number
- 45 is a Caprica number.
- 45 squared (45 * 45) equals 2025.
- 2025 splits into 20 and 25.
- 20 + 25 results in 45, the original number.
Java Code Implementation Overview
- The code checks for Caprica numbers and prints them in a range.
- It converts the number to a string to find the digit count.
- Squaring the number is the next step in the check.
Finding the Right Side Digits
Math.powcalculates powers of 10.- The square is divided to find the remainder, representing right-side digits.
Math.pow(10, l)calculates 10 to the power of the digits (l).
Finding the Left Side Digits
- Dividing the square finds the quotient, representing left-side digits.
Math.powdivides by 10 to the power of the number of digits.
Summing and Checking
- The right and left side digits get added.
- This sum is compared to the original number.
- If equal, it's a Caprica number returning
true; otherwise, it returnsfalse.
isCaprica Method
- A method checks if a number is Caprica.
- The
isCapricamethod returns a boolean (trueorfalse).
Main Method and Range Printing
- A
mainmethod prints Caprica numbers within a range (a and b). - A loop iterates from a to b (inclusive).
- The
isCapricamethod checks each number. - The method is static, so an object is not needed.
Printing Caprica Numbers
- If
isCapricareturnstrue, the number with "is a Caprica number" is printed. - An example range is 1 to 500.
Example Output
- The program identifies Caprica numbers in the range.
- Caprica numbers include 1, 9, 45, 55, 99, and 297, and more.
Verification
- 9 serves as an example for verifying Caprica numbers.
- 9 squared is 81; 8 + 1 = 9, which is the original number.
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