Lesson 2.3. Floating point numbers

Float type

The floating type allows to store decimal numbers. Its ful lname is floating point numbers. There are 2 types for encoding decimal numbers in C. As for the integers, it is advisable to choose the appropriate type to minimize the use of memory usage:

Type	Bytes	Bits	Minimum	Maximum
float	4	32	±10-37	±10+37
double	8	64	±10-307	±10+307
long double	16	128	±10-308	±10+308

Note: Float types do not support the unsigned prefix. Therefore, the unsigned float or unsigned double types do not exist in C.

Encoding of floats

We won't go into detail about how decimal numbers are encoded in memory. However, it is always interesting to know. If you are interested in this concept, you can consult this video which explains the details of the IEEE 754 standard.

Just remember two important things:

• The precision of floats is not infinite, for example with a float, 10¹⁰ is approximated by 99999997952.
• The larger the encoded numbers are, the less accurate they are.

To go further, the video below explains the origins and consequences of these inaccuracies:

Notation

The notation of decimal numbers in C is governed by a few rules:

• A float must have a dot: 12.45 -24. 3.1415
• The dot cannot be replaced by a comma.
• When the integer part is zero, it can be omitted: 0.25 can be written .25.
• The exponent is written e or E, e.g. 10e6 or 10E6.

Format codes

As for integers, you must use the appropriate format code to display a float. Here are the format codes for each type:

Type	Format code
float	%f
double	%lf
long double	%Lf

Exercises

Exercise 1

Here is an example that display a double :

#include <stdio.h>

int main(void) {

  // Declare and display the variable N
  double N=10e10;
  printf ("%lf", N);

  return 0;
}

Replace the type of the variable N with a float and change the format code of the printf. What do you notice?

#include <stdio.h> int main(void) { // Declare and display the variable N double N = 10e10; printf("%lf", N); return 0; }

Exercise 2

Write a program that declares a variable gold_number of type double and initializes it with the value 1.6180 before displaying it.

#include <stdio.h>

int main(void) {
    // Declare the golden number
    // COMPLETE HERE

    // Display the golden number
    // COMPLETE HERE

    return 0;
}

#include <stdio.h> int main(void) { // Declare the golden number // COMPLETE HERE // Display the golden number // COMPLETE HERE return 0; }

Exercise 3

Write a program that declares 2 variables a and b of types float and double respectively. The two variables are initialized with the value \(-10^{28}\) then displayed.

#include <stdio.h>

int main(void) {
  // Declare two variables (float and double)
  // COMPLETE HERE

  // Display the variables
  // COMPLETE HERE

  return 0;
}

#include <stdio.h> int main(void) { // Declare two variables (float and double) // COMPLETE HERE // Display the variables // COMPLETE HERE return 0; }

Quiz

Which types are used to store decimal numbers?

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How much space does a long double take in memory?

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Which type allows to memorize the greatest number?

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The estimated number of atoms in the universe is \( 10^{80} \). Which type is best suited to store this number?

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Which type will be the most precise?

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To store a number between -100 and +100, what is the advantage of using a double rather than a float?

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See also

• Learn C programming
• Lesson 1.1. History of C programming language
• Lesson 1.2. First program
• Lesson 1.3. Compilation
• Lesson 1.4. Preprocessor directives
• Lesson 1.5. Which compiler to choose?
• Lesson 1.6. Flowchart
• Lesson 2.1. Types and variables
• Lesson 2.2. Integers
• Lesson 2.4. Characters
• Lesson 2.5. Variables initialization
• Lesson 2.6. Ariane flight 501
• Lesson 3.1. Arithmetic operators
• Lesson 3.2. modulo
• Lesson 3.3. Operators and types
• Lesson 3.4. Type casting
• Lesson 3.5. Bitwise operators
• Lesson 3.6. Bitwise operators details
• Lesson 3.7. Shifting operators
• Lesson 3.8. Assignment operators
• Lesson 3.9. Increment and decrement operators
• Lesson 3.10. Comparison operators
• Lesson 3.11. Logical operators
• Lesson 3.12. Operator precedence
• Lesson 4.1. printf
• Lesson 4.2. scanf
• Lesson 4.3. putchar
• Lesson 5.1. Conditional branching (if...else)
• Lesson 5.2. Nested if and indentation
• Lesson 5.3. Checking intervals
• Lesson 5.4. Ternary Operator ?:
• Lesson 5.5. switch..case statement
• Lesson 5.6. Break keyword in switch..case
• Lesson 6.1. do..while loop in C
• Lesson 6.2. While loop in C
• Lesson 6.3. For loop in C
• Lesson 6.4. How to choose the right loop in C ?
• Lesson 6.5. Exercices on loops in C
• Lesson 7.1. Bit masking
• Lesson 7.2. Bit masking, how to clear a bit in C?
• Lesson 7.3. Bit masking, how to set a bit in C?
• Lesson 7.4. Bit masking, how to toggle a bit in C?
• Lesson 7.5. Bit masking, how to check a single bit in C?
• Lesson 7.6. Overview of bit masking
• Lesson 8.1. Basic syntax of C functions
• Lesson 8.2. Calling C functions
• Lesson 8.3. Void keyword
• Lesson 8.4. Return keyword
• Lesson 8.5. Variable scope
• Lesson 8.6. Global variables
• Lesson 8.7. Static variables
• Lesson 8.8. Random numbers in C
• Lesson 8.9. Mathematical functions in C
• Lesson 9.1. Syntax of C arrays
• Lesson 9.2. Array initialization
• Lesson 9.3. Multidimensional arrays
• Lesson 9.4. How C arrays are stored in memory?
• Lesson 9.5. Arrays and functions
• Lesson 9.6. Exercises on C arrays
• Lesson 10.1. Strings in C
• Lesson 10.2. Null terminated string
• Lesson 10.3. The string.h library
• Lesson 10.4. String and functions
• Lesson 11.1. Introduction to pointers in C
• Lesson 11.2. Syntax of C pointers
• Lesson 11.3. Dynamic memory allocation
• Lesson 11.4. Incrementing pointers
• Lesson 11.5. Pointers as function argument in C
• Lesson 12.1. Introduction to structures in C
• Lesson 12.2. Properties of structures in C
• Lesson 12.3. Structures and pointers
• Lesson 12.4. Structures and functions
• Lesson 13.1. Recursive functions in C
• Lesson 13.2. Depth of recursive functions
• Lesson 13.2. Mutual recursion
• Lesson 14.1. Additional exercises

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