How to Use Large Numbers in Scratch

This tutorial shows how to work with large numbers in Scratch. In this tutorial, numbers may be larger than 1e+21 (1 with 21 zeroes after it)—the limit above which Scratch automatically converts numbers to scientific notation. Instead of using default arithmetic blocks (which round and use scientific notation) on large numbers, these scripts work with numbers' digits to get accurate results.

This method works by displaying the number as a string. This will make the number display normally, no matter now large it is.

Note:

These blocks work only with positive integers.

Preparation

Variables

• (carry): The digit carried.
• (result): This will store the result.
• (a index): Which digit of (a) to use.
• (b index): Which digit of (b) to use.
• (num): A partial answer.

Blocks

• define (a) + (b): Addition
• define (a) - (b): Subtraction
• define (a) × (b): Multiplication
• define (a) ÷ (b): Division

Scripts

Addition

define (a) + (b)
set [a index v] to (length of (a))
set [b index v] to (length of (b))
set [carry v] to [0]
set [result v] to []
repeat until <<<(a index) < [1]> and <(b index) < [1]>> and <(carry) = [0]>>
  set [num v] to (((letter (a index) of (a)) + (letter (b index) of (b))) + (carry))
  set [result v] to (join ((num) mod (10)) (result))
  set [carry v] to ([floor v] of ((num) / (10)))
  change [a index v] by (-1)
  change [b index v] by (-1)
end

Subtraction

define (a) - (b)
set [a index v] to (length of (a))
set [b index v] to (length of (b))
set [carry v] to [1] // carry = 0 will mean borrowing
set [result v] to []
repeat until <<(a index) < [1]> and <(b index) < [1]>>
  set [num v] to (((letter (a index) of (a)) - (letter (b index) of (b))) + ((9) + (carry)))
  set [result v] to (join ((num) mod (10)) (result))
  set [carry v] to ([floor v] of ((num) / (10)))
  change [a index v] by (-1)
  change [b index v] by (-1)
end

Multiplication

define (a) × (b)
set [a index v] to (length of (a))
set [b index v] to (length of (b))
set [carry v] to [0]
set [result v] to []
repeat until <<((a index) + (b index)) < [2]> and <(carry) = [0]>>
  if <(b index) < [1]> then
    change [a index v] by ((b index) - (1))
    set [b index v] to [1]
  end
  set [num v] to (carry)
  repeat until <<(a index) < [1]> or <(b index) > (length of (b))>>
    change [num v] by ((letter (a index) of (a)) * (letter (b index) of (b)))
    change [a index v] by (-1)
    change [b index v] by (1)
  end
  set [result v] to (join ((num) mod (10)) (result))
  set [carry v] to ([floor v] of ((num) / (10)))
  set [b index v] to (((b index) - (1)) - ((length of (a)) - (a index)))
  set [a index v] to (length of (a))
end

Division

Note:

(carry:: variables) will give the remainder.

define (a) ÷ (b)
if <(b) = (0)> then // Checks for a division by 0
  set [result v] to [NaN]
  set [carry v] to [NaN]
  stop [this script v]
end
set [a index v] to [0]
set [carry v] to []
repeat until <not<(b:: custom) > (carry)>>
  change [a index v] by (1)
  set [carry v] to (join (carry) (letter (a index) of (a)))
end
set [result v] to []
repeat (((length of (a)) - (a index)) + (1))
  change [a index v] by (1)
  set [result v] to (join (result) ([floor v] of ((carry) / (b))))
  set [carry v] to (join ((carry) mod (b)) (letter (a index) of (a)))
end