Numbers and Math

Math Functions and Constants

The dart:math library adds common math helpers on top of the int/double operators: max(a, b) and min(a, b) pick the larger or smaller of two values; sqrt(x) returns the square root as a double; pow(x, y) raises one number to another; the constant pi is the IEEE-754 double closest to the true value. Combine pi, round(), and / to format a fixed-decimal approximation without a printf.

Program

Play the program to compare two numbers, take a square root, raise a power, and round pi to two decimal places.

dart_math.dart
Replay: real traced execution (multi-file project)
import 'dart:math';

void main() {
  var biggest = max(12, 7);
  var smallest = min(12, 7);
  var root = sqrt(144);
  var cube = pow(2, 10);
  var rounded = (pi * 100).round() / 100;
  print('$biggest $smallest $root $cube $rounded');
}

  1. biggest ← 12 (int)

    3void main() {4  var biggest = max(12, 7);5  var smallest = min(12, 7);
    values this step12 (int)biggest

  2. smallest ← 7 (int)

    4var biggest = max(12, 7);5var smallest = min(12, 7);6var root = sqrt(144);
    values this step7 (int)smallest

  3. root ← 12.0 (double)

    5var smallest = min(12, 7);6var root = sqrt(144);7var cube = pow(2, 10);
    values this step12.0 (double)root

  4. cube ← 1024 (num)

    6var root = sqrt(144);7var cube = pow(2, 10);8var rounded = (pi * 100).round() / 100;
    values this step1024 (num)cube

  5. rounded ← 3.14 (double)

    7var cube = pow(2, 10);8var rounded = (pi * 100).round() / 100;9print('$biggest $smallest $root $cube $rounded');
    values this step3.14 (double)rounded3.141592653589793pi

  6. print('$biggest $smallest $root $cube $rounded');

    8  var rounded = (pi * 100).round() / 100;9  print('$biggest $smallest $root $cube $rounded');10}
    output12 7 12.0 1024 3.14
    values this step12biggest7smallest12.0root1024cube3.14rounded

Follow the Values

  1. max(12, 7) gives 12.
  2. min(12, 7) gives 7.
  3. sqrt(144) gives 12.0.
  4. pow(2, 10) gives 1024.
  5. Rounded pi gives 3.14, so the program prints 12 7 12.0 1024 3.14. | expression | result | | --- | --- | | max(12, 7) | 12 | | min(12, 7) | 7 | | sqrt(144) | 12.0 | | pow(2, 10) | 1024 | | rounded pi | 3.14 |
max and min `max(a, b)` and `min(a, b)` return whichever operand wins; when both operands are `int`, the result stays `int`.
sqrt and pow `sqrt(x)` returns a `double` square root; `pow(x, y)` returns `num` and picks `int` automatically when both operands are non-negative `int`.
pi `pi` is the IEEE-754 `double` closest to the true value of pi. `(pi * 100).round() / 100` builds a 2-decimal approximation without `toStringAsFixed`.

Exercise: dart_math.dart

Reproduce 12 7 12.0 1024 3.14, then match each printed value to the expression that produced it.