color(blue)("Determine the decimal equivalent of "7/8)
Write as 7-:8
As 7 is less than 8 convert the 7 into tenth's so we have
for 10^("ths")" "-> " "70-:8 =color(magenta)( 8 ) " remainder " 6
Giving " "color(magenta)(0.8) + "remainder of "6/10
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Think of remainder 6/10" as "60/100
for 100^("ths") " "->" "60-:8 = color(magenta)(7) " remainder "4
Giving color(magenta)(0.87) +" remainder of "4/100
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Think of remainder 4/100" as "40/1000
for 1000^("ths")" "->" "40-:8 = color(magenta)(5) " remainder 0"
Giving color(magenta)(0.875) +" remainder of "0/1000
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
As there are no more remainders we stop
" "color(green)("So "7/8 ->7-:8 = 0.875" exactly")
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Determine the percentage equivalent of "7/8)
color(brown)("Using the shortcut method")
Multiply the decimal by 100
0.875xx100 = 87.5 This is the 87.5 from 87.5/100
color(brown)("Some people say you should write this as:")
0.875xx100% = 87.5% color(red)(larrcancel(" This is wrong"))
color(red)("I have been looking for this answer for ages. Changed my mind.")color(red)("It is correct. Just accept that for now. Hopefully you will")color(red)("understand why it is correct later.")
See https://socratic.org/s/aQHGq6ik for a better explanation about handling percentage symbols.
What it should look like is:
color(white)("dddd")ul(bar(|color(white)("d") 0.875xx100 = 87.5 -> 87.5/100 = 87.5%color(white)("d")|))
This is the same as: color(blue)(x)color(green)( color(white)("d")ubrace(xx1/100))
color(white)("ddddddddddddddddd.d") color(green)(darr)
color(white)("ddddddddddddddd")color(blue)(x) color(white)("dd")color(green)(%)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If you write: 0.875xx100%
you are in fact stating: 0.875xx100xx1/100 = 0.875
