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, \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- 
 

1. Discard all digits to the right of n^th significant digit.
2. 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++ 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 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);
    }
}

# 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 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
?>

<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)