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

  • Difficulty Level : Expert
  • Last Updated : 14 Apr, 2021

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 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 <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#




// 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 

This article is contributed by Mrigendra Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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