Question

How do you write `0.386` in scientific notation?

Answer 1

In scientific notation `0.386=3.86xx10^(-1)`

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of `10`.

Note that moving decimal `p` digits to right is equivalent to multiplying by `10^p` and moving decimal `q` digits to left is equivalent to dividing by `10^q`.

Hence, we should either divide the number by `10^p` i.e. multiply by `10^(-p)` (if moving decimal to right) or multiply the number by `10^q` (if moving decimal to left).

In other words, it is written as `axx10^n`, where `1<=a<10` and `n` is an integer.

To write `0,386` in scientific notation, we will have to move the decimal point one point to right, which literally means multiplying by `10`.

Hence in scientific notation `0.386=3.86xx10^(-1)` (note that as we have moved decimal one point to right we are multiplying by `10^(-1)`.

Answer 2

`3.86xx10^(-1)`

Explanation:

Given:`" "0.386`

`color(blue)("Point 1")`
Objective is to have just one none zero digit to the left of the decimal and everything else on the other side.

'........................................................................
`color(blue)("Point 2")`
If you multiply a value by 1 you do not change its 'intrinsic' value. However, 1 comes in many forms. For example:

`" "2/2"; "4/4"; "sqrt(7)/sqrt(7)"; "(-1)/(-1)"; "10/10`

So we can multiply by 1 and not change the intrinsic value but we can change the way it looks.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering your question")`

Multiply by 1 but in the form of `1=10/10` giving:

`0.386xx10/10`

This is the same as: `(0.386xx10)xx1/10`

Which is the same as: `(3.86)xx1/10" "larr" nearly there!"`

Another way of writing `xx1/10" is " xx10^(-1)`

So `3.86xx1/10" "->" "3.86xx10^(-1)`

So `0.386" is the same as "3.86xx10^(-1)`