Question

How do you write `1764.9` in scientific notation?

Answer 1

`1.7649xx10^3`

Explanation:

The objective is to have just one non zero digit to the left of the decimal and the rest of the numbers to the right. This changes the value so a correction has to be built, shown but not applied. In this case the correction is `(xx10^3)`

`color(brown)("With practice you will be able to do this in a lot less lines")`

Showing what is happening 1 stage at a time

`color(blue)("Stage 1")`
Multiply by 1 but in the form of `color(magenta)(1=10/10)`

`1764.9color(magenta)(xx10/10)" " =" " 1764.9/(color(magenta)(10))color(magenta)( xx 10)" " =" " 176.49xx10`
'.................................................................................................

`color(blue)("Stage 2")`
Multiply by 1 but in the form of `color(magenta)(1=10/10)`

`176.49xx10color(magenta)(xx10/10)" " =" "176.49/10xx10^2" " =" " 17.69xx10^2`
'..............................................................................................

`color(blue)("Stage 3")`
Multiply by 1 but in the form of `color(magenta)(1=10/10)`

`17.649xx10^2 color(magenta)(xx10/10)`

`=17.649/10xx10^3" "=" "color(blue)(1.7649xx10^3)`