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,
Significant digits include all the digits in a number falling in one of the following categories –
- All non-zero digits.
- Zero digits which-
- lie between significant digits.
- lie to the right of decimal point and at the same time to the right of a non-zero digit.
- 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 nth significant digit.
- 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++ 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)