Question

How do you write `9.277\times 10^ { 5}` in standard notation?

Answer 1

A slightly different way of thinking about it

927700

Explanation:

Given: `9.277xx10^5`

`color(green)("Note that "10^0=1 )`

Keep the decimal place where it is and slide the `9277` left for 5 digits. Use 0 as a place keeper

`color(white)(99999)ul(9.277xx10^5 larr" starting point")`
`color(white)(9999)92.77xx10^4 larr" "9.277xx10^5" moved left 1 place"`
`color(white)(999)927.7xx10^3 larr" "9.277xx10^5" moved left 2 places"`
`color(white)(..)9277.0xx10^2 larr" "9.277xx10^5" moved left 3 places"`
`color(white)(.)92770.0xx10^1 larr" "9.277xx10^5" moved left 4 places"`
`927700.0xx10^0 larr" "9.277xx10^5" moved left 4 places"`
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A lot of people say 'move the decimal point. I prefer it as above.
This is my reason

By example consider 6. This is in units so is 6.0
Multiply by 10 and you are now counting in tens, and tens are one place to the left. So were there was a 6 units becomes 0 units and where there where 0 tens there are now 6. So effectively the digits have shifted left by one place.

The thinking approach about this is down to individual's preference. As long as you get the correct answer; as stated in one of Terry Pratchett's books: What the heck!