Lesson 6. Real numbers
After reading lesson 6, you’ll be able to
- Use two types of real numbers
- Understand the memory-versus-precision trade-off
- Work around rounding errors in your piggy bank
Computers store and manipulate real numbers like 3.14159 using the IEEE-754 floating-point standard. Floating-point numbers can be very large or incredibly small: think galaxies and atoms. With such versatility, programming languages like JavaScript and Lua get by using floating-point numbers exclusively. Computers also support integers for whole numbers, the subject of the next lesson.
Consider this
Imagine a carnival game with three cups. The nearest cup is worth $0.10 to $1.00, the next is worth $1 to $10, and the farthest cup is worth $10 to $100. Choose one cup and toss as many as 10 coins. If landing four coins in the middle cup is worth $4, how would you win $100?
To represent many possible real numbers with a fixed amount of space, a floating-point number is like choosing 1 of 2,048 cups and placing anywhere from one to several trillion coins in it. Some bits represent a cup or bucket, and other bits represent the coins or offset within that bucket.