Floating Point Numbers

Floating Point Numbers

Whole numbers aren't enough - we need fractions, prices, distances, and physics. That's where floating point numbers come in.

float and double

A floating point number has a decimal part (like 3.14159). C++ offers two common sizes:

• float - 4 bytes, about 7 decimal digits of precision.
• double - 8 bytes, about 15 decimal digits of precision.

float pi = 3.14f;
double pi2 = 3.14159265358979;

The trailing f on the float marks it as a float (otherwise 3.14 is a double). Double is the default for decimal literals.

Scientific notation

Big and tiny numbers can use a shorthand like e notation:

double speedOfLight = 3e8;     // 3 x 10^8 = 300,000,000
double small = 1.5e-3;         // 0.0015

e8 means "times 10 to the 8th"; e-3 means "times 10 to the minus 3rd".

The precision gotcha

Floating point can't represent every decimal exactly. Some numbers (like 0.1) become tiny approximations, so:

double x = 0.1 + 0.2;   // not exactly 0.3!

It prints something like 0.30000000000000004. This is normal and expected - don't test floating point numbers for exact equality.

When to use which

• Use double by default: precision is usually worth the extra 4 bytes.
• Use float when memory is tight (big arrays of numbers) and rough precision is fine.
• Use integers when you only ever need whole numbers.

TL;DR

• float holds ~7 decimal digits; double holds ~15.
• double is the default for decimal literals and the usual first choice.
• Scientific notation: 3e8 means 300,000,000.
• Floating point numbers are approximations - never test exact equality.