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round() in C++

round is used to round off the given digit which can be in float or double. It returns the nearest integral value to provided parameter in round function, with halfway cases rounded away from zero. Instead of round(), std::round() can also be used . Header files used -> cmath, ctgmath Syntax :

Parameters: x, value to be rounded
double round (double x);
float round (float x);
long double round (long double x);
double round (T x);           
// additional overloads for integral types

Returns: The value of x rounded to the nearest 
integral (as a floating-point value).

Time Complexity: O(1)

Space Complexity: O(1)

lround( ) – The lround( ) function in C++ rounds the integer value that is nearest to the argument, with halfway cases rounded away from zero. The value returned is of type long int. It is similar to the round() function, but returns a long int whereas round returns the same data type as the input. It takes the same parameters as that of round( ) function.

llround( ) – The llround( ) function in C++ rounds the integer value that is nearest to the argument, with halfway cases rounded away from zero. The value returned is of type long long int. It is similar to the lround( ) function, but returns a long long int whereas lround( ) returns long int. It also takes the same parameters as that of round( ) function.




<div id="highlighter_673382" class="syntaxhighlighter nogutter  "><table border="0" cellpadding="0" cellspacing="0"><tbody><tr><td class="code"><div class="container"><div class="line number1 index0 alt2"><code class="comments">// C++ code to demonstrate the round( ), lround( ), llround( ) functions</code></div><div class="line number2 index1 alt1"><code class="preprocessor">#include <iostream></code></div><div class="line number3 index2 alt2"><code class="preprocessor">#include <cmath></code></div><div class="line number4 index3 alt1"> </div><div class="line number5 index4 alt2"><code class="keyword bold">using</code> <code class="keyword bold">namespace</code> <code class="plain">std;</code></div><div class="line number6 index5 alt1"><code class="undefined spaces"> </code> </div><div class="line number7 index6 alt2"><code class="comments">// Driver program</code></div><div class="line number8 index7 alt1"><code class="color1 bold">int</code> <code class="plain">main() { </code></div><div class="line number9 index8 alt2"><code class="undefined spaces">     </code><code class="comments">// initializing value</code></div><div class="line number10 index9 alt1"><code class="undefined spaces">     </code><code class="color1 bold">double</code> <code class="plain">x = 32.14, y = 12.552, z = 91.78;</code></div><div class="line number11 index10 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"Nearest value of "</code> <code class="plain"><< x << </code><code class="string">" : "</code> <code class="plain"><< round(x) << </code><code class="string">"\n"</code><code class="plain">;</code></div><div class="line number12 index11 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"Nearest value of "</code> <code class="plain"><< y << </code><code class="string">" : "</code> <code class="plain"><< round(y) << </code><code class="string">"\n"</code><code class="plain">;</code></div><div class="line number13 index12 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"Nearest value of "</code> <code class="plain"><< z << </code><code class="string">" : "</code> <code class="plain"><< round(z) << </code><code class="string">"\n\n"</code><code class="plain">;</code></div><div class="line number14 index13 alt1"><code class="undefined spaces">     </code> </div><div class="line number15 index14 alt2"><code class="undefined spaces">     </code><code class="comments">/**** Positive Floating Number of decimal value less than 0.5 *****/</code></div><div class="line number16 index15 alt1"><code class="undefined spaces">     </code><code class="plain">x = 0.14, y = 21.48, z = 0.075;</code></div><div class="line number17 index16 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"round("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< round(x);</code></div><div class="line number18 index17 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< round(y);</code></div><div class="line number19 index18 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< round(z) << endl;</code></div><div class="line number20 index19 alt1"><code class="undefined spaces">  </code> </div><div class="line number21 index20 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"lround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< lround(x);</code></div><div class="line number22 index21 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< lround(y);</code></div><div class="line number23 index22 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< lround(z) << endl;</code></div><div class="line number24 index23 alt1"><code class="undefined spaces">  </code> </div><div class="line number25 index24 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"llround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< llround(x);</code></div><div class="line number26 index25 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< llround(y);</code></div><div class="line number27 index26 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< llround(z) << endl << endl;</code></div><div class="line number28 index27 alt1"><code class="undefined spaces">   </code> </div><div class="line number29 index28 alt2"><code class="undefined spaces">     </code><code class="comments">/**** Positive Floating Number of decimal value greater than 0.5 ****/</code></div><div class="line number30 index29 alt1"><code class="undefined spaces">     </code><code class="plain">x = 0.85, y = 25.73, z = 91.553;</code></div><div class="line number31 index30 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"round("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< round(x);</code></div><div class="line number32 index31 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< round(y);</code></div><div class="line number33 index32 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< round(z) << endl;</code></div><div class="line number34 index33 alt1"><code class="undefined spaces">  </code> </div><div class="line number35 index34 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"lround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< lround(x);</code></div><div class="line number36 index35 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< lround(y);</code></div><div class="line number37 index36 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< lround(z) << endl;</code></div><div class="line number38 index37 alt1"><code class="undefined spaces">  </code> </div><div class="line number39 index38 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"llround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< llround(x);</code></div><div class="line number40 index39 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< llround(y);</code></div><div class="line number41 index40 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< llround(z) << endl << endl;</code></div><div class="line number42 index41 alt1"><code class="undefined spaces">     </code> </div><div class="line number43 index42 alt2"><code class="undefined spaces">     </code><code class="comments">/**** Positive Floating Number of decimal value 0.5 ****/</code></div><div class="line number44 index43 alt1"><code class="undefined spaces">     </code><code class="plain">x = 0.50, y = 25.5, z = 91.500;</code></div><div class="line number45 index44 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"round("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< round(x);</code></div><div class="line number46 index45 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< round(y);</code></div><div class="line number47 index46 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< round(z) << endl;</code></div><div class="line number48 index47 alt1"><code class="undefined spaces">  </code> </div><div class="line number49 index48 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"lround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< lround(x);</code></div><div class="line number50 index49 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< lround(y);</code></div><div class="line number51 index50 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< lround(z) << endl;</code></div><div class="line number52 index51 alt1"><code class="undefined spaces">  </code> </div><div class="line number53 index52 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"llround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< llround(x);</code></div><div class="line number54 index53 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< llround(y);</code></div><div class="line number55 index54 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< llround(z) << endl << endl;</code></div><div class="line number56 index55 alt1"><code class="undefined spaces">     </code> </div><div class="line number57 index56 alt2"><code class="undefined spaces">     </code><code class="comments">/**** Negative Floating Number of decimal value less than 0.5 ****/</code></div><div class="line number58 index57 alt1"><code class="undefined spaces">     </code><code class="plain">x = -0.14, y = -0.002, z = -23.39;</code></div><div class="line number59 index58 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"round("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< round(x);</code></div><div class="line number60 index59 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< round(y);</code></div><div class="line number61 index60 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< round(z) << endl;</code></div><div class="line number62 index61 alt1"><code class="undefined spaces">  </code> </div><div class="line number63 index62 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"lround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< lround(x);</code></div><div class="line number64 index63 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< lround(y);</code></div><div class="line number65 index64 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< lround(z) << endl;</code></div><div class="line number66 index65 alt1"><code class="undefined spaces">  </code> </div><div class="line number67 index66 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"llround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< llround(x);</code></div><div class="line number68 index67 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< llround(y);</code></div><div class="line number69 index68 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< llround(z) << endl << endl;</code></div><div class="line number70 index69 alt1"><code class="undefined spaces">   </code> </div><div class="line number71 index70 alt2"><code class="undefined spaces">     </code><code class="comments">/**** Negative Floating Number of decimal value greater than 0.5 ****/</code></div><div class="line number72 index71 alt1"><code class="undefined spaces">     </code><code class="plain">x = -0.72, y = -21.864, z = -57.62;</code></div><div class="line number73 index72 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"round("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< round(x);</code></div><div class="line number74 index73 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< round(y);</code></div><div class="line number75 index74 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< round(z) << endl;</code></div><div class="line number76 index75 alt1"><code class="undefined spaces">  </code> </div><div class="line number77 index76 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"lround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< lround(x);</code></div><div class="line number78 index77 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< lround(y);</code></div><div class="line number79 index78 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< lround(z) << endl;</code></div><div class="line number80 index79 alt1"><code class="undefined spaces">  </code> </div><div class="line number81 index80 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"llround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< llround(x);</code></div><div class="line number82 index81 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< llround(y);</code></div><div class="line number83 index82 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< llround(z) << endl << endl;</code></div><div class="line number84 index83 alt1"><code class="undefined spaces">     </code> </div><div class="line number85 index84 alt2"><code class="undefined spaces">     </code><code class="comments">/**** Negative Floating Number of decimal value of 0.5 ****/</code></div><div class="line number86 index85 alt1"><code class="undefined spaces">     </code><code class="plain">x = -0.5, y = -6.50, z = -56.500;</code></div><div class="line number87 index86 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"round("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< round(x);</code></div><div class="line number88 index87 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< round(y);</code></div><div class="line number89 index88 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"round("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< round(z) << endl;</code></div><div class="line number90 index89 alt1"><code class="undefined spaces">  </code> </div><div class="line number91 index90 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"lround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< lround(x);</code></div><div class="line number92 index91 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< lround(y);</code></div><div class="line number93 index92 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"lround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< lround(z) << endl;</code></div><div class="line number94 index93 alt1"><code class="undefined spaces">  </code> </div><div class="line number95 index94 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"llround("</code> <code class="plain"><< x << </code><code class="string">") = "</code> <code class="plain"><< llround(x);</code></div><div class="line number96 index95 alt1"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< y << </code><code class="string">") = "</code> <code class="plain"><< llround(y);</code></div><div class="line number97 index96 alt2"><code class="undefined spaces">     </code><code class="plain">cout << </code><code class="string">"\t\t"</code> <code class="plain"><< </code><code class="string">"llround("</code> <code class="plain"><< z << </code><code class="string">") = "</code> <code class="plain"><< llround(z) << endl;</code></div><div class="line number98 index97 alt1"><code class="undefined spaces">     </code> </div><div class="line number99 index98 alt2"><code class="undefined spaces">     </code><code class="keyword bold">return</code> <code class="plain">0;</code></div><div class="line number100 index99 alt1"><code class="plain">}</code></div></div></td></tr></tbody></table></div>

Output
...d(0.075) = 0
lround(0.14) = 0    lround(21.48) = 21        lround(0.075) = 0
llround(0.14) = 0    llround(21.48) = 21        llround(0.075) = 0

round(0.85) = 1        round(25.73) = 26        round(91.553) = 92
lround(0.85) = 1    lround(25.73) = 26        lround(91.553) = 92
llround(0.85) = 1    llround(25.73) = 26        llround(91.553) = 92

round(0.5) = 1        round(25.5) = 26        round(91.5) = 92
lround(0.5) = 1        lround(25.5) = 26        lround(91.5) = 92
llround(0.5) = 1    llround(25.5) = 26        llround(91.5) = 92

round(-0.14) = -0    round(-0.002) = -0        round(-23.39) = -23
lround(-0.14) = 0    lround(-0.002) = 0        lround(-23.39) = -23
llround(-0.14) = 0    llround(-0.002) = 0        llround(-23.39) = -23

round(-0.72) = -1    round(-21.864) = -22    round(-57.62) = -58
lround(-0.72) = -1    lround(-21.864) = -22    lround(-57.62) = -58
llround(-0.72) = -1    llround(-21.864) = -22    llround(-57.62) = -58

round(-0.5) = -1    round(-6.5) = -7        round(-56.5) = -57
lround(-0.5) = -1    lround(-6.5) = -7        lround(-56.5) = -57
llround(-0.5) = -1    llround(-6.5) = -7        llround(-56.5) = -57

Here, in the above program we have just calculated the nearest integral value of given float or double value. which has been calculated accurately.

Possible Applications

  1. Handling the mismatch between fractions and decimal : One use of rounding numbers is shorten all the three’s to the right of the decimal point in converting 1/3 to decimal. Most of the time, we will use the rounded numbers 0.33 or 0.333 when we need to work with 1/3 in decimal. We usually work with just two or three digits to the right of the decimal point when there is no exact equivalent to the fraction in decimal.
  2. Changing multiplied result : There will be difference between multiplication of 25, 75 and 0.25, 0.75 we get 0.875 .We started with 2 digits to the right of the decimal point and ended up with 4. Many times we will just round up the result to 0.19 . 




// C++ code for above explanation
#include <cmath>
#include <iostream>
using namespace std;
 
// Driver program
int main()
{
    // Initializing values for int type
    long int a1 = 25, b1 = 30;
 
    // Initializing values for double type
    double a2 = .25, b2 = .30;
    long int ans_1 = (a1 * b1);
    double ans_2 = (a2 * b2);
 
    // Rounded result for both
    cout << "From first multiplication :" << round(ans_1) << "\n";
    cout << "From second multiplication :" << round(ans_2) << "\n";
    return 0;
}

Output
From first multiplication :750
From second multiplication :0
  1. Fast calculation : Suppose in need of fast calculation we take approx value and then calculate nearest answer. For example, we get an answer 298.78 after any calculation and by rounding off we get an absolute answer of 300.
  2. Getting estimate : Sometimes you want to round integers instead of decimal numbers. Usually you are interested in rounding to the nearest multiple of 10, 100, 1, 000 or million. For example, in 2006 the census department determined that the population of New York City was 8, 214, 426. That number is hard to remember and if we say the population of New York City is 8 million it is a good estimate because it doesn’t make any real difference what the exact number is.

Official references –

Reference : www.mathworksheetcenter.com, www.cplusplus.com


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