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

Last Updated : 16 Feb, 2023

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, \frac{22}{7} = 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-

Discard all digits to the right of n^th significant digit.
If this discarded number is-
- less than half a unit in n^thplace, leave the n^th digit unchanged.
- greater than half a unit in the n^th place, increase the n^th digit by unity.
- exactly half a unit in the n^th place, increase the n^th 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 <bits/stdc++.h> 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# 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

<?php // PHP program to round-off // a number to given no. of // significant digits  // Function to round -  // off the number function Round_off($N, $n) {          $h;     $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 = $b + 0.5;     if ($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 ?>

JavaScript

<script>  // Javascript program to round-off a number to given no. of // significant digitsimport   // Function to round - off the number function Round_off(N , n) {     var h;     var l, a, b, c, d, e, i, j, m, f, g;     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 = parseInt(b / 10);      d = n - i;     b = N;     b = b * Math.pow(10, d);     e = b + 0.5;     if (e == Math.ceil(b)) {         f = (Math.ceil(b));         h = parseInt(f - 2);         if (h % 2 != 0) {             e = e - 1;         }     }     j = Math.floor(e);     m = Math.pow(10, d);     j = j / m;     document.write("The number after rounding-off is "                        + j); }  // Driver main function var 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 contributed by Princi Singh   </script>

Output:

The number after rounding-off is 139.6

Time complexity: O(logN)

Space complexity: O(1)

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

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

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