# Round-off a number to a given number of significant digits

Given a positive number n (n > 1), round-off this number to a given no. of significant digits, d.

Examples:

Input : n = 139.59
d = 4
Output : The number after rounding-off is 139.6 .

The number 139.59 has 5 significant figures and for rounding-off
the number to 4 significant figures, 139.59 is converted to 139.6 .

Input : n = 1240
d = 2
Output : The number after rounding-off is 1200 .



What are significant figures?

Each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first non-zero digit, are called as significant figures.

Since there are numbers with large number of digits, for example, = 3.142857143, so in order to limit such numbers to a manageable number of digits, we drop unwanted digits and this process is called rounding off.

Significant digits include all the digits in a number falling in one of the following categories –

• All non-zero digits.
• Zero digits which-
1. lie between significant digits.
2. lie to the right of decimal point and at the same time to the right of a non-zero digit.
3. are specifically indicated to be significant.

The following table shows numbers and no. of significant digits present in them – Rules for Rounding-off a Number

To round off a number to n significant figures-

1. Discard all digits to the right of nth significant digit.
2. If this discarded number is-
• less than half a unit in nthplace, leave the nth digit unchanged.
• greater than half a unit in the nth place, increase the nth digit by unity.
• exactly half a unit in the nth place, increase the nth digit by unity if its odd, otherwise leave it unchanged.

The following table shows rounding-off a number to a given no. of significant digits – ## C++

 // C++ program to round-off a number to given no. of  // significant digits  #include  using namespace std;     // Function to round - off the number  void Round_off(double N, double n)  {      int h;      double l, a, b, c, d, e, i, j, m, f, g;      b = N;      c = floor(N);         // Counting the no. of digits to the left of decimal point      // in the given no.      for (i = 0; b >= 1; ++i)          b = b / 10;         d = n - i;      b = N;      b = b * pow(10, d);      e = b + 0.5;      if ((float)e == (float)ceil(b)) {          f = (ceil(b));          h = f - 2;          if (h % 2 != 0) {              e = e - 1;          }      }      j = floor(e);      m = pow(10, d);      j = j / m;      cout << "The number after rounding-off is " << j;  }     // Driver main function  int main()  {      double N, n;         // Number to be rounded - off      N = 139.59;         // No. of Significant digits required in the no.      n = 4;         Round_off(N, n);      return 0;  }

## Java

 // Java program to round-off a number to given no. of  // significant digits     import java.io.*;  import static java.lang.Math.*;  public class A {         // Function to round - off the number      static void Round_off(double N, double n)      {          int h;          double l, a, b, c, d, e, i, j, m, f, g;          b = N;          c = floor(N);             // Counting the no. of digits to the left of decimal point          // in the given no.          for (i = 0; b >= 1; ++i)              b = b / 10;             d = n - i;          b = N;          b = b * pow(10, d);          e = b + 0.5;          if ((float)e == (float)ceil(b)) {              f = (ceil(b));              h = (int)(f - 2);              if (h % 2 != 0) {                  e = e - 1;              }          }          j = floor(e);          m = pow(10, d);          j = j / m;          System.out.println("The number after rounding-off is "                            + j);      }         // Driver main function      public static void main(String args[])      {          double N, n;             // Number to be rounded - off          N = 139.59;             // No. of Significant digits required in the no.          n = 4;             Round_off(N, n);      }  }

## Python3

 # Python 3 program to round-off a number   # to given no. of significant digits  from math import ceil, floor, pow    # Function to round - off the number  def Round_off(N, n):      b = N      c = floor(N)         # Counting the no. of digits       # to the left of decimal point       # in the given no.      i = 0;      while(b >= 1):          b = b / 10         i = i + 1        d = n - i      b = N      b = b * pow(10, d)      e = b + 0.5     if (float(e) == float(ceil(b))):          f = (ceil(b))          h = f - 2         if (h % 2 != 0):              e = e - 1     j = floor(e)      m = pow(10, d)      j = j / m      print("The number after rounding-off is", j)     # Driver Code  if __name__ == '__main__':             # Number to be rounded - off      N = 139.59        # No. of Significant digits       # required in the no.      n = 4        Round_off(N, n)     # This code is contributed by  # Surendra_Gangwar

## C#

 // C# program to round-off a number   // to given no. of significant digits  using System;     class A {         // Function to round - off the number      static void Round_off(double N, double n)      {          int h;          double b, d, e, i, j, m, f;          b = N;          // c = Math.Floor(N);             // Counting the no. of digits to the          // left of decimal point in the given no.          for (i = 0; b >= 1; ++i)              b = b / 10;             d = n - i;          b = N;          b = b * Math.Pow(10, d);          e = b + 0.5;          if ((float)e == (float)Math.Ceiling(b)) {              f = (Math.Ceiling(b));              h = (int)(f - 2);              if (h % 2 != 0) {                  e = e - 1;              }          }          j = Math.Floor(e);          m = Math.Pow(10, d);          j = j / m;          Console.WriteLine("The number after " +                          "rounding-off is " + j);      }         // Driver main function      public static void Main()      {          double N, n;             // Number to be rounded - off          N = 139.59;             // No. of Significant digits required in the no.          n = 4;             Round_off(N, n);      }  }     // This code is contributed by vt_m.

## PHP

 = 1; ++$i)   $b = $b / 10;     $d = $n - $i;      $b = $N;      $b = $b * pow(10, $d);   $e = $b + 0.5;   if ($e == ceil($b))   {   $f = (ceil($b));   $h = $f - 2;   if ($h % 2 != 0)           {              $e = $e - 1;          }      }      $j = floor($e);      $m = pow(10, $d);      $j = $j / $m;   echo "The number after rounding-off is " ,$j;  }         // Driver Code      $N; $n;         // Number to be rounded - off      $N = 139.59;     // No. of Significant digits   // required in the no.   $n = 4;         Round_off($N, $n);     // This code is contributed by anuj_67  ?>

Output:

The number after rounding-off is 139.6


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Improved By : vt_m, SURENDRA_GANGWAR

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