Order of magnitude calculation

[Nikhil faraday]

I am confused! . In some books it is written that if the multiplier is less than 3.162 , the order of the magnitude of the number is the power of the ten in scientific notation , while in some books it is written less than 5 . What is right? Help!

 

[Nugatory]

I am confused! . In some books it is written that if the multiplier is less than 3.162 , the order of the magnitude of the number is the power of the ten in scientific notation , while in some books it is written less than 5 . What is right? Help!

Either one. 5 is midway between one and ten on a linear scale while 3.162 is midway between one and ten on a logarithmic scale, and you'll get good results either way. If you're doing classroom exercises, do it the way your professor says.

It is more important that you keep track of how many of these close rounding choices you've made in each direction as you work through the estimation than that any single rounding choice be perfect.