Scratch_Andy_DE wrote:

Hi,

The operators multiplication and division returns wrong results when calculation with point numbers.
For example the result of 2.3 x 6 is 13.799999999999999 in place of 13.8.
And reversed the result of 13.8 / 6 is 2.3000000000000003 in place of 2.3.
When I set a variable with this result they shows 13.8 respectively 2.3.
But the length of this variable is 18.
And the blocks “Say” and “Think” shows also different results of this variable. Say shows 13.8 respective 2.3 and Think 13.799999999999999 respective 2.3000000000000003

ResExsention wrote:

Scratch_Andy_DE wrote:

Hi,

The operators multiplication and division returns wrong results when calculation with point numbers.
For example the result of 2.3 x 6 is 13.799999999999999 in place of 13.8.
And reversed the result of 13.8 / 6 is 2.3000000000000003 in place of 2.3.
When I set a variable with this result they shows 13.8 respectively 2.3.
But the length of this variable is 18.
And the blocks “Say” and “Think” shows also different results of this variable. Say shows 13.8 respective 2.3 and Think 13.799999999999999 respective 2.3000000000000003

Scratch isn't wrong. Scratch is just rounding off the variables for some reason.

Not sure how to overcome this, perhaps the variables may not have enough bytes?

Scratch_Andy_DE wrote:

ResExsention wrote:

Scratch_Andy_DE wrote:

Hi,

The operators multiplication and division returns wrong results when calculation with point numbers.
For example the result of 2.3 x 6 is 13.799999999999999 in place of 13.8.
And reversed the result of 13.8 / 6 is 2.3000000000000003 in place of 2.3.
When I set a variable with this result they shows 13.8 respectively 2.3.
But the length of this variable is 18.
And the blocks “Say” and “Think” shows also different results of this variable. Say shows 13.8 respective 2.3 and Think 13.799999999999999 respective 2.3000000000000003

Scratch isn't wrong. Scratch is just rounding off the variables for some reason.

Not sure how to overcome this, perhaps the variables may not have enough bytes?

It is not necessary to round something because 2.3*6 is always exactly 13.8.
The results of multiplication and division are definitely wrong.

#include <iostream>
int main(){std::cout << 2.3 * 6 << std::endl;}

0.30000000000000004.com wrote:

It's actually pretty simple. When you have a base 10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1/2, 1/4, 1/5, 1/8, and 1/10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. In binary (or base 2), the only prime factor is 2. So you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1/2, 1/4, 1/8 would all be expressed cleanly as decimals. While, 1/5 or 1/10 would be repeating decimals. So 0.1 and 0.2 (1/10 and 1/5) while clean decimals in a base 10 system, are repeating decimals in the base 2 system the computer is operating in. When you do math on these repeating decimals, you end up with leftovers which carry over when you convert the computer's base 2 (binary) number into a more human readable base 10 number.

Flowermanvista wrote:

This is actually normal - it's because of the number format Scratch uses, which is a double precision floating point number. Double floats, as they are called, are able to represent a very wide range of numbers from very small to absolutely massive, but only with about 15 digits of accuracy.

The classic example is adding 0.1 + 0.2, which equates to 0.30000000000000004, instead of 0.3 as expected. To paraphrase a Scratcher named TheLogFather, the issue is that the number 0.3 doesn't exist as the computer sees it. If you end up going from Scratch to more serious languages, you'll have to learn to code around these limitations.

Here's a quote from 0.30000000000000004.com, which I think gives a really good explanation of this:

0.30000000000000004.com wrote:

It's actually pretty simple. When you have a base 10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1/2, 1/4, 1/5, 1/8, and 1/10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. In binary (or base 2), the only prime factor is 2. So you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1/2, 1/4, 1/8 would all be expressed cleanly as decimals. While, 1/5 or 1/10 would be repeating decimals. So 0.1 and 0.2 (1/10 and 1/5) while clean decimals in a base 10 system, are repeating decimals in the base 2 system the computer is operating in. When you do math on these repeating decimals, you end up with leftovers which carry over when you convert the computer's base 2 (binary) number into a more human readable base 10 number.