# 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-
- 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 n
^{th}significant digit. - If this discarded number is-
- less than half a unit in n
^{th}place, 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.

- less than half a unit in n

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; ` `} ` |

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## 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); ` ` ` `} ` `} ` |

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## 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. ` |

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## 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 ` `?> ` |

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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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