Back of the envelope calculations help.

[nascentmind]

Hi,

How do I develop and train to do quick back of the envelope calculations? How have you developed these techniques? I am not quick in it and make silly mistakes.

 

[jim hardy]

force yourself to rigorously write down each step, as you did in junior high school math.

perhaps i have advantage - grew up in days of slide rule where first thiing you had to reduce a problem to something manageable. And you had to keep track of decimal point yourself.
An early complaint when calculators came around was ''The kids don't think anymore. If they divide twelve by sixty and get twenty for an answer, they don't question it."

So it's a question of developing good habits.
Always do reasonability checks.

Haste makes waste.

 

[nascentmind]

perhaps i have advantage - grew up in days of slide rule where first thiing you had to reduce a problem to something manageable. And you had to keep track of decimal point yourself.

That's the exact problem I have i.e. keeping track of decimal points and also the 0's.

 

[jim hardy]

""That's the exact problem I have i.e. keeping track of decimal points and also the 0's.""

we are rushed today in everything we do. i think it's the computers...

form the habit of writing all your numbers in scientific notation,
so when you multiply or divide you're dealing with numbers arout 0.1 to 10 .

then collect the exponents.

always do them on paper (that's what the envelope is for)
and NEATLY paying attention to alignment.. (Do they teach mechanical drafting in jr high anymore?)

And do them twice for cross-check. That avoids a lot of embarassment.

Henry Thoreau said: "The most valuable thing a man can possess
is a determination not to be hurried."

old jim

 

[alphy]

I can understand the importance of being able to do quick back of the envelope calculations. These calculations can help us estimate and approximate results in a timely manner, especially when we don't have access to advanced tools or data. To develop and train in this skill, there are a few tips I can offer.

Firstly, practice makes perfect. The more you practice doing these calculations, the better you will become at it. Start with simple calculations and gradually move on to more complex ones. This will help you build your confidence and accuracy in performing these calculations.

Secondly, make sure you have a solid understanding of the concepts and equations involved in the calculation. This will help you identify which equations to use and how to manipulate them to get the desired result. It also helps to have a good grasp of basic math operations like multiplication, division, and estimation.

Another helpful technique is to break the calculation down into smaller, simpler steps. This can help prevent silly mistakes and make the overall process more manageable. Additionally, double-checking your work and using estimation techniques can also help catch any errors that may have been made.

As for how I have developed these techniques, it has been through years of practice and experience in my field. I have also found it helpful to work with colleagues and discuss different approaches and methods for doing back of the envelope calculations. Collaborating and learning from others can be a valuable tool in honing this skill.

In conclusion, developing and training to do quick back of the envelope calculations takes practice, solid understanding of concepts and equations, breaking down the calculation, and double-checking your work. With time and dedication, you can improve your speed and accuracy in performing these calculations.