Question

If a sample of a chemical weighed 2.00 g before heating, and 1.60 g after heating, what is the mass of the matter lost?

Answer 1

`0.4g`

Explanation:

We can take the ending weight, subtract that from the starting weight, and see how much was lost:

`color(white)(++0)2.00`
`color(white)--1.60`

it works out to 0.4g

Answer 2

The mass of the matter lost is 0.4 grams

Explanation:

Given:`" "2.00-1.60`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Approach method 1")`

this is the same as

`[2+0/10+0/100]-[1+6/10+0/100]`

making the subtraction easier write
`[2+0/10+0/100]" as "[1+10/10+0/100]`

So we have:

`" "1+10/10+0/100`

`" "ul(1+6/10+0/100) larr" Subtract"`
`" "0+4/10+0" "` which is the same as `0.40`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Approach method 2 - this is the one they expect you to use.")`

Introducing a lot of spacing to make things more readable

Initial condition presented as:

`" "2." "color(white)(.)0color(white)(....)0`
`" "ul(1." "color(white)(.)6" "0)" "larr" Subtract"`

'.....................................................................................
`color(brown)("Step 1 - Making the numbers easier to deal with")`

'borrow' 1 from the 2 and put it in the `10^("ths")` column, but 1 is worth 10 of `10^("ths")` so we have:

`" "1.""color(white)(....)10color(white)(....)0`
`" "ul(1." "color(white)(.)6" "0)" "larr" Subtract"`

'.....................................................................................
`color(brown)("Step 2 - doing the subtraction")`

`" "1.""color(white)(....)10color(white)(....)0`
`" "ul(1." "color(white)(.)6" "0)" "larr" Subtract"`
`" "0. color(white)(.......)4color(white)(....)0`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("This is how approach method 2 should look like")`

`" "cancel(2)^1. color(white)(..)cancel(0)^(10)color(white)(..)0`
`" "ul(1 ." "color(white)(.)6 color(white)(.......)0) " "larr " Subtract"`
`color(white)(....) 0 . color(white)(.....) 4color(white)(2....) 0`