Question

How to get the Nth digit after the decimal point of a floating-point number in C++

Answer 1

#include <iostream>
#include <string>
#include <iomanip>
#include <cmath>
#include <stdexcept>
 
/**
 * Returns the Nth digit after the decimal point.
 *
 * Examples:
 * getNthDecimalDigit(123.456789, 1) -> 4
 * getNthDecimalDigit(123.456789, 2) -> 5
 * getNthDecimalDigit(123.456789, 3) -> 6
 *
 * @param value    The floating-point number to inspect.
 * @param position The digit position after the decimal point (1-based).
 * @return The Nth digit after the decimal point.
 *
 * @throws std::invalid_argument if position is less than 1.
 */
int getNthDecimalDigit(double value, int position)
{
    if (position < 1) {
        throw std::invalid_argument(
            "Position must be a positive integer.");
    }
 
    // Convert to positive value
    value = std::abs(value);
 
    // Convert number to string
    std::string str = std::to_string(value);
 
    // Find decimal point
    std::size_t decimalPos = str.find('.');
 
    // No decimal point found
    if (decimalPos == std::string::npos) {
        return 0;
    }
 
    // Index of the requested digit
    std::size_t digitIndex = decimalPos + position;
 
    // Return 0 if the digit does not exist
    if (digitIndex >= str.length()) {
        return 0;
    }
 
    return str[digitIndex] - '0';
}
 
int main()
{
    const double number = 123.456789;

    std::cout << std::fixed
              << std::setprecision(6)
              << number
              << '\n';
 
    for (int position = 1; position <= 6; ++position) {
        std::cout
            << position
            << " digit after decimal: "
            << getNthDecimalDigit(number, position)
            << std::endl;
    }
 
    std::cout << "\nAdditional Examples:\n";
 
    std::cout
        << "2nd digit of 98.7654: "
        << getNthDecimalDigit(98.7654, 2)
        << std::endl;
 
    std::cout
        << "3rd digit of -12.345: "
        << getNthDecimalDigit(-12.345, 3)
        << std::endl;
 
    std::cout
        << "5th digit of 1.2: "
        << getNthDecimalDigit(1.2, 5)
        << std::endl;
}
 
 
/*
run:
 
123.456789
1 digit after decimal: 4
2 digit after decimal: 5
3 digit after decimal: 6
4 digit after decimal: 7
5 digit after decimal: 8
6 digit after decimal: 9

Additional Examples:
2nd digit of 98.7654: 6
3rd digit of -12.345: 5
5th digit of 1.2: 0
 
*/
 

 

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Answer 2

#include <iostream>
#include <string>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <stdexcept>

/**
 * Returns the Nth digit after the decimal point.
 *
 * Examples:
 * getNthDecimalDigit(123.456789, 1) -> 4
 * getNthDecimalDigit(123.456789, 2) -> 5
 * getNthDecimalDigit(123.456789, 3) -> 6
 *
 * @param value    Floating-point number.
 * @param position Digit position after the decimal point (1-based).
 * @return The requested digit, or 0 if it does not exist.
 *
 * @throws std::invalid_argument if position < 1.
 */
int getNthDecimalDigit(double value, int position)
{
    if (position < 1)
    {
        throw std::invalid_argument(
            "Position must be greater than 0.");
    }

    // Convert the absolute value to a string with high precision
    std::ostringstream oss;
    oss << std::fixed
        << std::setprecision(15)
        << std::abs(value);

    std::string str = oss.str();

    // Find the decimal point
    std::size_t decimalPos = str.find('.');

    if (decimalPos == std::string::npos)
    {
        return 0;
    }

    // Locate the requested digit
    std::size_t digitIndex = decimalPos + position;

    if (digitIndex >= str.length())
    {
        return 0;
    }

    return str[digitIndex] - '0';
}

int main()
{
    const double number = 123.456789123456789;

    std::cout << std::fixed
              << std::setprecision(16)
              << number
              << '\n';

    // Print the first 15 digits after the decimal point
    for (int i = 1; i <= 15; ++i)
    {
        std::cout
            << i
            << " digit after decimal = "
            << getNthDecimalDigit(number, i)
            << '\n';
    }

    std::cout << "\nAdditional Examples\n";
    std::cout << "-------------------\n";

    std::cout
        << "123.456789, position 4 -> "
        << getNthDecimalDigit(123.456789, 4)
        << '\n';

    std::cout
        << "-98.7654, position 2 -> "
        << getNthDecimalDigit(-98.7654, 2)
        << '\n';

    std::cout
        << "1.2, position 5 -> "
        << getNthDecimalDigit(1.2, 5)
        << '\n';

    return 0;
}

// 123.456789123456789 original number
// 123.456789123456787

/*
run:

123.4567891234567867
1 digit after decimal = 4
2 digit after decimal = 5
3 digit after decimal = 6
4 digit after decimal = 7
5 digit after decimal = 8
6 digit after decimal = 9
7 digit after decimal = 1
8 digit after decimal = 2
9 digit after decimal = 3
10 digit after decimal = 4
11 digit after decimal = 5
12 digit after decimal = 6
13 digit after decimal = 7
14 digit after decimal = 8
15 digit after decimal = 7

Additional Examples
-------------------
123.456789, position 4 -> 7
-98.7654, position 2 -> 6
1.2, position 5 -> 0

*/

 

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