#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#
