If the number you are calculating will be used as a lower bound, then rounding all the items up to the nearest 10s place and then using a little factoring can get one to the go/nogo solution.
"can't be more than X"
or
"can't be less than Y"
are powerful devices that allow one to keep thinking, rather than making tasks to be done later. But like the article mentions in the comments, if precision is warranted, then one needs to slow down and double check their work.
As mentioned in the preface to Street Fighting Mathematics, "How to Solve It" by George Polya is another very approachable book. This tl;dr is pretty good [1] (aside, this book should be in the public domain by now)
"can't be more than X"
or
"can't be less than Y"
are powerful devices that allow one to keep thinking, rather than making tasks to be done later. But like the article mentions in the comments, if precision is warranted, then one needs to slow down and double check their work.
As mentioned in the preface to Street Fighting Mathematics, "How to Solve It" by George Polya is another very approachable book. This tl;dr is pretty good [1] (aside, this book should be in the public domain by now)
[1] https://math.ucr.edu/~res/math138A-2012/polya.pdf
There are other books that train folks on how to do mental mathematics like
* The Trachtenberg Speed System of Basic Mathematics https://www.abebooks.com/products/isbn/9780285629165/3011837...
* Secrets of Mental Math https://www.abebooks.com/products/isbn/9780307338402
I found this neat publication from the American Mathematical Society on Back of the Envelope calculation.
https://www.ams.org/publications/TEXT-33-chap-1.pdf