Question

How do you simplify `9.594 div 0.06`?

Answer 1

A way to get round the decimal place in the initial division expression.

`159.9`

Explanation:

Note that `9.594` is the same as `9594xx1/1000`

Note that `0.06` is the same as `6xx1/100`

So `9.594-:0.006` is the same as `[9594-:6]xx[1/1000-:1/100]`

`(9594-:6)xx1/10`

I will do the division first then multiply by the `1/10` at the very end

`" "9594`
`color(magenta)(1000)xx6->ul(6000) larr" subtract"`
`" "3594`
`color(magenta)(color(white)(1)500)xx6->ul(3000) larr" subtract"`
`" "594`
`color(magenta)(color(white)(10)90)xx6->ul(color(white)(0)540)larr" subtract"`
`" "color(white)(0)54`
`color(magenta)(color(white)(100)9)xx6->" "ul(54) larr" subtract"`
`" "0`

As we have 0 we may now stop the division

`9594-:6 = color(magenta)(1599)`

Now we multiply by the `1/10` giving:

`159.9`
~~~~~~~~~~~~~~~~~~~~~~~~~~~

If the division had not finished with a 0 at that point then we would have gone into decimal values.

Answer 2

`= 159.6`

Explanation:

The rule with dividing BY a decimal is simple ... DON'T!!

You can change any decimal into a whole number by multiplying by a power of `10`

Write the division as a fraction:

`9.594/0.06`

Multiply the numerator and the denominator by the same number

`9.594/color(blue)(0.06) color(red)(xx 100/100)" "larr [color(red)(100/100 =1)]`

This changes the denominator into a whole number:

`=959.4/color(blue)(6)" "larr` divide as usual

`6|ul(9" "^3 5" "^5 9." "^5 4)`
`color(white)(xx)1color(white)(x.x)5color(white)(xxx)9. color(white)(x.)6" "larr` details below

`= 159.6`

`9 div 6 = 1 " carry " 3`
`35 div 6 = 5 " carry " 5`
`59 div 6 = 9 " carry " 5`
`54div 6 = 9` , no remainder