Question

How do you simplify `9.44\times 70.8`?

Answer 1

`668.352`

Explanation:

`9.44 xx 70.8`

`:.=9 44/100 xx 70 8/10`

`:.=944/100 xx 708/10`

`:.=668352/1000`

`:.=668.352`

Answer 2

`9.44 xx 70.8 = 668.352`

Explanation:

You can do long multiplication.

Ignore the decimal places for now:

`color(white)(...........)944`
`color(white)(...........)ul(color(blue)(7)0color(red)(8))`
`color(white)(..........)color(red)(7552)" "` multiply the top row by `color(red)(3)`
`color(white)(.......)ul(color(blue)(660800)" "` multiply the top row by `color(blue)(700)`
`color(white)(.......)ul(668352)" "`add the two rows

(There was no point in multiplying by the middle number, 0)

Now count how many decimal places there were altogether in the original numbers. There were `3` places.

`9color(red)(.44) xx 70color(red)(.8) = 668color(red)(.352)`

There must be the same number of places in the final answer.

As a final check, do a quick estimate of the size of the answer.
`9 xx 70 = 630`

An answer of `668` is in the right order of size.