# 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;` `}` |

## 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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