Question

How do you express the number in standard form: `6.6 x 10^8`?

Answer 1

`660000000.0 x`

Explanation:

`color(blue)("Step 1")`

Separate out the `x` and the numbers so that you have:

`6.6xx10^8xx x`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 2")`

Consider just the numbers.

An effective way of showing what happens next is by taking it 1 step at a time. Basically for each x10 we 'slide' the number towards the left 1 place whilst keeping the decimal point where it is.

`6.6xx1color(white)(..)=" "6.6`
`6.6xx10color(white)(.) = " "66.0 larr" moved left 1 place"`
`6.6xx10^2= " "660.0 larr" moved left 2 places"`
`6.6xx10^3=" "6600.0 larr" moved left 3 places"`
`6.6xx10^4=" "66000.0 larr" moved left 4 places"`
`6.6xx10^5=" "660000.0 larr" moved left 5 places"`
`color(red)(" "darr)`
`color(red)(" until we get")`
`color(red)(" "darr)`
`6.6xx10^8=" "660000000.0 larr" moved left 8 places"`

Think of:

`6.6" as counting in units"`
`66.0" as counting in tens "->" 6 tens + 6 units"`

The switch from counting in units to 10's means that what was units shifts to the left and becomes 10's. This process of shifting the numbers left is repeated for each of the `xx10`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 3")`

Put it all together:

`660000000.0 x`

`color(red)("Other people will tell you to move the decimal point. Whilst this")`
`color(red)("gives the same affect it does not reflect what is actually happening")`