Exact Numbers
Why 1/3 stays 1/3: fractions, square roots and big numbers are kept exact, and decimals only appear when you ask.
- Fractions stay fractions
- Square roots
- Big numbers
- When decimals appear
- Asking for a decimal
- Letters as symbols
Fractions stay fractions
Every number is kept exactly. 1/3 + 1/6 is 1/2, and even 0.1 + 0.2 is exactly 3/10 -- the rounding error other calculators show never happens.
Square roots
Square roots are simplified and kept exact: sqrt(8) is 2sqrt(2), and sqrt(2)*sqrt(2) is exactly 2.
Big numbers
Whole numbers have no size limit: every digit of 2^100 or 30! is correct.
When decimals appear
Some values have no exact form -- pi, e, sin(1), ln(2). These are approximations and show 10 significant digits. Anything worked out from one is an approximation too.
Asking for a decimal
To see an exact number as a decimal, ask: decimal(x, digits) gives as many digits as you like, correctly, scientific uses powers of ten, float gives a quick approximation and repeating shows the repeating block.
Letters as symbols
A name that has no value yet is a symbol, so a formula written with it stays a formula you can differentiate, expand or solve.